EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ ${p}$-LAPLACIAN EQUATIONS

DOI10.1112/S0024609303002546zbMath1088.35025MaRDI QIDQ4460788

Shibo Liu, Shu-Jie Li

Publication date: 29 March 2004

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

existenceMorse theoryDirichlet problem fot the p-LaplacianTang index

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20)

Related Items (17)

Existence and multiplicity of solutions for asymptotically linear, noncoercive elliptic equations ⋮ Multiplicity results for some nonlinear elliptic problems with asymptotically \(p\)-linear terms ⋮ \(p\)-Laplacian problems with nonlinearities interacting with the spectrum ⋮ Nontrivial solutions of Kirchhoff type problems ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík type resonance at infinity. II ⋮ Resonant equations with the Neumann \(p\)-Laplacian plus an indefinite potential ⋮ Existence of radial solutions for an asymptotically linear \(p\)-Laplacian problem ⋮ Nonlinear versions of Stampacchia and Lax-Milgram theorems and applications to \(p\)-Laplace equations ⋮ Rotating periodic solutions for super-linear second order Hamiltonian systems ⋮ Multiplicity results for a class of quasilinear elliptic problems ⋮ NONTRIVIAL SOLUTIONS FOR N-LAPLACIAN EQUATIONS WITH SUB-EXPONENTIAL GROWTH ⋮ Multiple solutions for a BVP on \((0,+\infty)\) via Morse theory and \(H^1_{0,p}(\mathbb{R}^+)\) versus \(C^1_{p}(\mathbb{R}^+)\) local minimizers ⋮ Nontrivial solutions of superlinear \(p\)-Laplacian equations ⋮ Multiple solutions for asymptotically \((p-1)\)-homogeneous \(p\)-Laplacian equations ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík-type resonance at infinity. III ⋮ Multiple Solutions for p-Laplacian Type Problems with an Asymptotically p-linear Term ⋮ Multiple solutions for \(p\)-Laplacian type problems with asymptotically \(p\)-linear terms via a cohomological index theory

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