a
Prof. Dr. Thomas Bartsch — Publications
Book
Topological methods für variational problems with symmetries
Habilitationsschrift Heidelberg 1992
Lecture Notes in Mathematics 1560, Springer Verlag, Berlin Heidelberg, 1993

Papers and Preprints
The files to download are preprint versions and do not necessarily coincide with the printed versions.

[84] Asymptotically radial solutions in expanding annular domains. (with M. Clapp, M. Grossi, F. Pacella)
Preprint. Download as PDF.
[83] Poincaré-Hopf type formulas on convex sets of Banach spaces. (with E.N. Dancer)
Preprint. Download as PDF.
[82] On the Fucik spectrum for Schrödinger operators on R^N and applications (with Z.-Q. Wang, Z. Zhang)
Preprint. Download as PDF.
[81] A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system. (with E.N. Dancer, Z.-Q. Wang)
Preprint. Download as PDF.
[80] N-vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh-Poisson and the Lane-Emden-Fowler equations. (with A. Pistoia, T. Weth)
Preprint. Download as PDF.
[79] Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. (with P. Polacik and P. Quittner)
Journal of the European Mathematical Society (to appear). Download as PDF.
[78] Existence and multiplicity results for semipositone p-Laplacian problems with falling zeroes. (with R. Shivaji, Z. Zhang)
Preprint. Download as PDF.
[77] Solutions concentrating on higher dimensional subsets for singularly perturbed elliptic equations II. (with S. Peng)
Preprint. Download as PDF.
[76] Solutions concentrating on higher dimensional subsets for singularly perturbed elliptic equations I. (with S. Peng)
Indiana University Mathematics Journal 57 (2008), 1599-1632.
[75] Morse theory and applications to differential equations (with A. Szulkin and M. Willem).
Handbook of Global Analysis (D. Krupka, D. Saunders, Eds.), Elsevier 2008, 41-73.
[74] An invariant set generated by the domain topology for parabolic semiflows with small diffusion (with N. Ackermann, P. Kaplicky).
Discrete and Continuous Dynamical Systems 18 (2007), 613-626.
[73] Existence and non-existence of solutions to elliptic equations related to Caffarelli-Kohn-Nirenberg inequalities (with S. Peng, Z. Zhang).
Calculus of Variations and Partial Differential Equations 30 (2007), 113-136.
[72] Note on ground states of nonlinear Schrödinger systems (with Z.-Q. Wang).
Journal of Partial Differential Equations 19 (2006), 200-207
[71] On multibump semi-classical bound states of nonlinear Schrödinger equations with electromagnetic fields (with N. Dancer and S. Peng).
Advances in Differential Equations 11 (2006), 781-812.
[70]

Bound states for a coupled Schrödinger system (with Z.-Q. Wang and J. Wei).
Journal of Fixed Point Theory and Applications 2 (2007), 353-367.

[69] Semiclassical symmetric Schrödinger equations: existence of solutions concentrating simultaneously on several spheres (with S. Peng). Zeitschrift für angewandte Mathematik und Physik (ZAMP) 58 (2007), 778-804.
[68] Nodal solutions of nonlinear elliptic Dirichlet problems on radial domains (with M. Degiovanni).
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni 17 (2006), 69-85.
[67] Solutions of nonlinear Dirac equations (with Y. Ding).
Journal of Differential Equations 226 (2006), 210-249
[66] Configuration spaces, transfer, and 2-nodal solutions of a
semiclassical nonlinear Schrödinger equation
(with M. Clapp and T. Weth).
Mathematische Annalen 338 (2007), 147-185.
[65] On the existence and the profile of nodal solutions of elliptic
equations involving critical growth
(with A. M. Micheletti and A. Pistoia).
Calculus of Variations and Partial Differential Equations 26 (2006), 265-282
[64] The Dirichlet problem for superlinear elliptic equations (with
Z.-Q. Wang and M. Willem)
Handbook of Differential Equations - Stationary Partial Differential Equations,
Vol. 2 (M. Chipot, P. Quittner, Eds.), Elsevier 2005, 1-55.
[63] Hamiltonian systems: periodic and homoclinic solutions by
variational methods
(with A. Szulkin)
Handbook of Differential Equations - Ordinary Differential Equations,
Vol. 2 (A. Canada, P. Drabek, A. Fonda, Eds.), Elsevier 2005, 77-146.
[62] Existence and nonexistence results for critical growth polyharmonic elliptic systems (with Y. Guo)
Journal of Differential Equations 220 (2006), 531-543
[61] A Priori Bounds, Nodal Equilibria and Connecting Orbits in Indefinite Superlinear Parabolic Problems (with N. Ackermann, P. Kaplicky, P. Quittner). Transactions of the American Mathematical Society 360 (2008), 3493-3539.
[60] The effect of the domain’s configuration space on the number of nodal solutions of singularly perturbed elliptic equations (with T. Weth).
Topological Methods in Nonlinear Analysis 26 (2005), 109-133
[59] Deformation theorems on non-metrizable vector spaces and applications to critical point theory (with Y. Ding).
Mathematische Nachrichten 279 (2006), 1267-1288
[58] Partial symmetry of least energy nodal solutions to some variational
problems
(with T. Weth and M. Willem)
Journal d'Analyse Mathématique 96 (2005), 1-18.
[57]

Nodal solutions of a p-Laplacian equation (with Z. Liu and T. Weth)
Proceedings of the London Mathematical Society (3) 91 (2005), 129-152

[56] Three nodal solutions of singularly perturbed elliptic equations on domains without topology (with T. Weth)
Annales de l'Institut Henri Poincaré, Analyse nonlinéaire 22 (2005), 259-281.
[55]

Superstable manifolds of semilinear parabolic problems (with N. Ackermann)
Journal of Dynamics and Differential Equations 17 (2005), 115-173

[54] Multiple solutions to a critical polyharmonic equation. (with M. Schneider and T. Weth)
Journal für die reine und angewandte Mathematik 571 (2004), 131-143
[53]

Critical equations for the polyharmonic operator.
Topological Methods, Variational Methods and their Applications, H. Brezis, K.-C. Chang, S.-J. Li, P. Rabinowitz (eds.), World Scientific 2003, 35-43

[52]

Location and critical groups of critical points in Banach spaces with an application to nonlinear eigenvalue problems. (with Z. Liu)
Advances in Differential Equations 9 (2004), 645-676

[51] Multiple sign changing solutions of a quasilinear elliptic eigenvalue problem involving the p-Laplacian (with Z. Liu)
Communications in Contemporary Mathematics 6 (2004),245-258.
[50] On a superlinear elliptic p-Laplacian equation. (with Z. Liu)
Journal of Differential Equations 198 (2004), 149-175
[49] Sign changing solutions of superlinear Schrödinger equations. (with Z. Liu and T. Weth)
Communications in Partial Differential Equations 29 (2004), 25-42.
[48] A note on additional properties of sign changing solutions to superlinear elliptic equations. (with T. Weth)
Topological Methods in Nonlinear Analysis 22 (2003), 1-14
[47] A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator. (with T. Weth and M. Willem)
Calculus of Variations and Partial Differential Equations 18 (2003), 253-286.
[46] On a nonlinear Schrödinger equation with a deep potential well. (with A. Pankov and Z.-Q. Wang; in Russian)
Proceedings of the First Ukrainian Congress of Mathematics 2001,
Inst. Math, Nat. Acad. Sci. Ukraine, Kiev 2001, 5-14.
[45] Linking, positive invariance, and localization of critical points.
H. Brezis, S. J. Li, J. Q. Liu, and P. H. Rabinowitz (eds.), Morse Theory, Minimax Theory and Their Applications to Nonlinear Differential Equations, Lectures at the Morningside Center of Mathematics, Beijing 1999, International Press, Cambridge MA 2003, 9-21.
[44] Conley Index.
Encyclopaedia of Mathematics, Supplement III, M. Hazewinkel (Ed.), Kluwer Academic Publishers 2002, 110-112.
[43] Homoclinic solutions of an infinite-dimensional Hamiltonian system. (with Y. Ding)
Mathematische Zeitschrift 240 (2002), 289-310.
[42] Periodic solutions of superlinear beam and membrane equations with perturbations from symmetry. (with Y. Ding)
Nonlinear Analysis 44 (2001), 727-748.
[41] Critical point theory on partially ordered Hilbert spaces.
Journal of Functional Analysis 186 (2001), 117-152.
[40] Nonlinear Schrödinger equations with steep potential well. (with A. Pankov and Z.-Q. Wang)
Communications in Contemporary Mathematics 3 (2001), 549-569.
[39] Extremal sign changing solutions of semilinear Dirichlet problems.
in: K.-C. Chang and Y. Long (eds.), Progress in Nonlinear Analysis, Proceedings of the Second International Conference on Nonlinear Analysis, Tianjin 1999, World Scientific, Singapur 2000 , 1-10.
[38] On the Morse indices of sign changing solutions of nonlinear elliptic problems. (with K.-C. Chang and Z.-Q. Wang)
Mathematische Zeitschrift 233 (2000), 655-677.
[37] Multiple positive solutions of a nonlinear Schrödinger equation. (with Z.-Q. Wang)
Zeitschrift für angewandte Mathematik and Physik 51 (2000), 366-384.
[36] Critical point theory with applications to asymptotically linear wave and beam equations. (with Y. Ding)
Differential and Integral Equations 13 (2000), 973-1000.
[35] On a nonlinear Schrödinger equation with periodic potential. (with Y. Ding)
Mathematische Annalen 313 (1999), 15-37.
[34] Periodic solutions of a wave equation with concave and convex nonlinearities. (with Y. Ding and C. Lee)
Journal of Differential Equations 152 (1999), 121-141.
[33] Sign changing solutions of nonlinear Schrödinger equations. (with Z.-Q. Wang)
Topological Methods in Nonlinear Analysis 13 (1999), 191-198.
[32] Infinitely many solutions of nonlinear elliptic systems. (with D. G. de Figueiredo)
Progress in Nonlinear Differential Equations and Their Applications 35, J. Escher, C. Simonett (eds.), Birkhäuser, Basel 1998, 51-67.
[31] Critical point theory for asymptotically quadratic functionals and applications to problems with resonance. (with S. Li)
Nonlinear Analysis: Theory, Methods and Applications 28 (1997), 419-441.
[30] Periodic solutions of even Hamiltonian systems on the torus. (with Z.-Q. Wang)
Mathematische Zeitschrift 224 (1997), 65-76.
[29] Periodic solutions of spatially periodic, even Hamiltonian systems. (with Z.-Q. Wang)
Journal of Differential Equations 135 (1997), 103-128.
[28] A generalization of the Weinstein-Moser theorems on periodic solutions of a Hamiltonian system near an equilibrium.
Annales de l'Institut Henri Poincaré, Analyse nonlinéaire 14 (1997), 691-718.
[27] Even Hamiltonian systems on tori and cotangent spaces of tori. (with Z.-Q. Wang)
in: Nonlinear Analysis, Theory, Methods & Applications 30 (1997), 4123-4134. Proceedings of the Second World Congress of Nonlinear Analysts, Athens 1996.
[26] Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows.
Topology in Nonlinear Analysis, Banach Center Publications 35 (1996), 9-27.
[25] Borsuk-Ulam theorems, the Lusternik-Schnirelmann category and index theories.
in: Lakshmikantham (ed.), Proceedings of the First World Congress of Nonlinear Analysts, Tampa 1992, Vol. I, de Gruyter, Berlin New York 1996, 537-547.
[24] Radial and nonradial solutions of a nonlinear scalar field equation.
in: Lakshmikantham (ed.), Proceedings of the First World Congress of Nonlinear Analysts, Tampa 1992, Vol. III, de Gruyter, Berlin New York 1996, 2135-2146.
[23] Critical point theory for indefinite functionals with symmetries. (with M. Clapp)
Journal of Functional Analysis 138 (1996), 107-136.
[22] On the existence of sign changing solutions for semilinear Dirichlet problems. (with Z.-Q. Wang)
Topological Methods in Nonlinear Analysis 7 (1996), 115-131.
[21] Existence and multiplicity results for some superlinear elliptic problems on R^N. (with Z.-Q. Wang)
Communications in Partial Differential Equations 20 (1995), 1725-1741.
[20] On an elliptic equation with concave and convex nonlinearities. (with M. Willem)
Proceedings of the American Mathematical Society 123 (1995), 3555-3661.
[19] Periodic solutions of non-autonomous Hamiltonian systems with symmetries. (with M. Willem)
Journal für die reine und angewandte Mathematik 451 (1994), 149-159.
[18] A simple proof of the degree formula for Z/p-equivariant maps.
Mathematische Zeitschrift 212 (1993), 285-292.
[17] Infinitely many solutions of a symmetric Dirichlet Problem.
Nonlinear Analysis: Theory, Methods and Applications 20 (1993), 1205-1216.
[16] Infinitely many non-radial solutions of an Euclidean scalar field equation. (with M. Willem)
Journal of Functional Analysis 117 (1993), 447-460.
[15] Infinitely many radial solutions of a semilinear elliptic problem in R^n (with M. Willem)
Archive for Rational Mechanics and Analysis 124 (1993), 261-276.
[14] Bifurcation of steady states in a modified Belousov-Zhabotinskii reaction. (with M. Kern)
Topological Methods in Nonlinear Analysis 2 (1993), 105-124.
[13] The Conley index over a space.
Mathematische Zeitschrift 209 (1992), 167-177.
[12] On the existence of Borsuk-Ulam theorems.
Topology 31 (1992), 533-543.
[11] The compact category and multiple periodic orbits of symmetric starshaped Hamiltonian systems. (with M. Clapp)
Mathematische Annalen 293 (1992), 523-542.
[10] The global structure of the zero set of a family of semilinear Fredholm maps.
Nonlinear Analysis: Theory, Methods and Applications 17 (1991), 313-331.
[9] A mountain pass theorem for actions of compact Lie groups. (with M. Clapp and D. Puppe)
Journal für die reine und angewandte Mathematik 419 (1991), 55-66.
[8] The Leray-Schauder degree of $S^1$-equivariant operators associated to autonomous neutral equations in spaces of periodic functions. (with J. Mawhin)
Journal of Differential Equations 92 (1991), 90-99.
[7] On the genus of representation spheres.
Commentarii Mathematici Helvetici 65 (1990), 85-95.
[6] Bifurcation theory for symmetric potential operators and the equivariant cup-length. (with M. Clapp)
Mathematische Zeitschrift 204 (1990), 341-356.
[5] Critical points of symmetric functionals.
Manuscripta Mathematica 66 (1989), 129-152.
[4] Bifurcation theory for metric parameter spaces.
in B. Jiang (ed.), Topological Fixed Point Theory and Applications, Proceedings Tianjin 1988, Lecture Notes in Mathematics 1411, Springer-Verlag, Berlin Heidelberg 1989, 1-8
[3] A global index for bifurcation of fixed points.
Journal für die reine und angewandte Mathematik 391 (1988), 181-197.
[2] The role of the J-homomorphism in multiparameter bifurcation theory.
Bulletin des Sciences mathématiques, 2e série, 112 (1988), 177-184.
[1] Algebra im 13. Jahrhundert: Die Formel von Fibonacci.
Der mathematische und naturwissenschaftliche Unterricht 41 (1988), 463-465.