COMPUTATIONS OF THE COHOMOLOGY GROUPS WITH APPLICATIONS TO ASYMPTOTICALLY LINEAR BEAM EQUATIONS AND NONCOOPERATIVE ELLIPTIC SYSTEMS1*

DOI10.1081/PDE-120002784zbMath1019.35004OpenAlexW2064257477MaRDI QIDQ4532826

Wen Ming Zou

Publication date: 19 September 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120002784

zbMATH Keywords

filtrationcritical groups\({\mathcal E}\)-cohomologybeam equationnoncooperative elliptic systems

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (6)

Periodic solutions for an asymptotically linear wave equation with resonance ⋮ An infinite-dimensional linking theorem and applications ⋮ Computations of cohomology groups and nontrivial periodic solutions of Hamiltonian systems ⋮ Multiple solutions for asymptotically linear elliptic systems ⋮ Computations of critical groups and applications to asymptotically linear wave equation and beam equation ⋮ Multiplicity result for asymptotically linear noncooperative elliptic systems

Cites Work

• Two applications of a three critical points theorem
• Critical point theorems for indefinite functionals
• Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue
• The computations of the critical groups with an application to elliptic resonant problems at a higher eigenvalue
• A variational approach to subquadratic perturbations of elliptic systems
• Subharmonic solutions for subquadratic Hamiltonian systems
• Infinite dimensional Morse theory and multiple solution problems
• Cohomology and Morse theory for strongly indefinite functionals
• Applications of local linking to critical point theory
• A unified approach to a class of strongly indefinite functionals
• Critical point theory for indefinite functionals with symmetries
• Linking theorems and applications to semilinear elliptic problems at resonance
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• A Maximum Principle for an Elliptic System and Applications to Semilinear Problems
• Time periodic solutions to a semilinear beam equation
• Nontrivial periodic solutions of a nonlinear beam equation
• Variational elliptic problems which are nonquadratic at infinity
• Multiple critical points for asymptotically quadratic functionals
• An infinite dimensional Morse theory with applications
• A variational approach to noncooperative elliptic systems
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• Infinite dimensional cohomology groups and periodic solutions of asymptotically linear Hamiltonian systems

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