Trajectories joining critical points of nonlinear parabolic and hyperbolic partial differential equations

DOI10.1016/0022-0396(84)90107-4zbMath0529.35040OpenAlexW2091368374MaRDI QIDQ787388

Krzysztof P. Rybakowski

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(84)90107-4

zbMATH Keywords

existenceConley indexnonlinear Dirichlet boundary-value problemspositive time-independent solutionstrajectories joining critical points

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Second-order nonlinear hyperbolic equations (35L70) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (8)

A Morse equation in Conley's index theory for semiflows on metric spaces ⋮ Connecting orbits for nonlinear differential equations at resonance ⋮ Stationary solutions and connecting orbits for \(p\)-Laplace equation ⋮ An index product formula for the study of elliptic resonance problems ⋮ The existence of trajectories joining critical points ⋮ A homotopy index continuation method and periodic solutions of second- order gradient systems ⋮ Nontrivial solutions of elliptic boundary value problems with resonance at zero ⋮ Homotopy invariants methods in the global dynamics of strongly damped wave equation

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• The Morse index, repeller-attractor pairs and the connection index for semiflows on noncompact spaces
• Theory of functional differential equations. 2nd ed
• Limiting behavior of strongly damped nonlinear wave equations
• Global topological perturbations of nonlinear elliptic eigenvalue problems
• A Bifurcation Problem for a Nonlinear Hyperbolic Partial Differential Equation
• On the Homotopy Index for Infinite-Dimensional Semiflows
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Asymptotic states for equations of reaction and diffusion
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