Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the \(p\)-biharmonic

DOI10.1016/j.na.2012.07.015zbMath1252.35141OpenAlexW2067391756MaRDI QIDQ452441

Roberto Livrea, Pasquale Candito, Lin Li

Publication date: 21 September 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.07.015

zbMATH Keywords

critical point theoryinfinitely many solutionsNavier boundary value problem\(p\)-biharmonic type operators

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Weak solutions to PDEs (35D30) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (18)

Multiple solutions on a \(p\)-biharmonic equation with nonlocal term ⋮ Infinitely many solutions for a nonlinear Navier problem involving the p-biharmonic operator ⋮ Unnamed Item ⋮ Multiple solutions for a nonlocal elliptic problem involving \((p(x), q(x))\)-biharmonic operator ⋮ Existence and nonexistence for boundary problem involving the \(p\)-biharmonic operator and singular nonlinearities ⋮ Existence of three solutions for variable exponent elliptic systems ⋮ Existence results for perturbed fourth-order Kirchhoff type elliptic problems with singular term ⋮ Existence of multiple solutions for a quasilinear biharmonic equation ⋮ Unnamed Item ⋮ Existence of solutions for the discrete Dirichlet problem involving \(p\)-mean curvature operator ⋮ A critical \(p\)-biharmonic system with negative exponents ⋮ Infinitely many solutions for a class of indefinite biharmonic equation under symmetry breaking situations ⋮ Existence of two non-zero weak solutions for a nonlinear Navier boundary value problem involving the \(p\)-biharmonic ⋮ Ground states solutions for modified fourth-order elliptic systems with steep well potential ⋮ Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Existence of nontrivial weak solutions for \(p\)-biharmonic Kirchhoff-type equations

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• A general variational principle and some of its applications
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