Multiple critical points theorems without the Palais--Smale condition

DOI10.1016/j.jmaa.2004.06.034zbMath1071.34015OpenAlexW2008456423MaRDI QIDQ703894

Gabriele Bonanno

Publication date: 12 January 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.06.034

zbMATH Keywords

\(p\)-LaplacianCritical pointMultiple solutionsTwo-point boundary value problem

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear boundary value problems for ordinary differential equations (34B15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (16)

Multiplicity of solutions to a four-point boundary value problem of a differential system via variational approach ⋮ Nonlocal fractional \(p(\cdot)\)-Kirchhoff systems with variable-order: two and three solutions ⋮ Existence of solution of a three-point boundary value problem via variational approach ⋮ Variational approach for an elastic beam equation with local nonlinearities ⋮ Variational Approaches to a Discrete Elliptic Problem with a Weight ⋮ Three periodic solutions for \(p\)-Hamiltonian systems ⋮ CRITICAL POINT APPROACHES FOR IMPULSIVE STURM-LIOUVILLE DIFFERENTIAL EQUATIONS WITH NONLINEAR DERIVATIVE DEPENDENCE ⋮ Multiplicity of solutions for a nonlocal elliptic system of \((p,q)\)-Kirchhoff type ⋮ Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities ⋮ Variational approaches to Kirchhoff-type second-order impulsive differential equations on the half-line ⋮ Discrete fourth-order boundary value problems with four parameters ⋮ Infinitely many solutions for a class of p-Laplacian equation with Sturm-Liouville type nonhomogeneous boundary conditions ⋮ Multiple positive solutions of second-order Sturm-Liouville boundary value problems for impulsive differential equations ⋮ Two solutions to a nonlinear Neumann problem without asymptotic conditions ⋮ Critical point approaches to generalized Yamabe equations on Riemannian manifolds and applications to Emden-Fowler problems ⋮ A mountain pass theorem for a suitable class of functions

Cites Work

• Unnamed Item
• Some remarks on a three critical points theorem
• Existence of multiple solutions for second order boundary value problems
• Three symmetric positive solutions for a second-order boundary value problem
• On a three critical points theorem
• Nonlinear boundary value problems with multiple solutions.
• A three critical points theorem and its applications to the ordinary Dirichlet problem
• A general variational principle and some of its applications
• THREE SOLUTIONS FOR A QUASILINEAR TWO-POINT BOUNDARY-VALUE PROBLEM INVOLVING THE ONE-DIMENSIONAL p-LAPLACIAN
• Multiple symmetric positive solutions for a second order boundary value problem

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