Existence and multiplicity of positive solutions for a fourth-order elliptic equation

DOI10.1017/prm.2018.145zbMath1437.35387OpenAlexW2911616720MaRDI QIDQ5221053

Marcelo F. Furtado, Giovany M. Figueiredo, João Pablo P. da Silva

Publication date: 27 March 2020

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/prm.2018.145

zbMATH Keywords

variational methodscritical nonlinearitiesfourth-order problems

Mathematics Subject Classification ID

Higher-order elliptic equations (35J30) Variational methods for higher-order elliptic equations (35J35) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (2)

Fourth-order elliptic problems involving concave-superlinear nonlinearities ⋮ Existence of nontrivial solutions for modified nonlinear fourth-order elliptic equations with indefinite potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A fourth-order equation with critical growth: the effect of the domain topology
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Symmetry properties in systems of semilinear elliptic equations
• On a class of nonlinear Schrödinger equations
• Existence and nonexistence results for critical growth biharmonic elliptic equations
• Elliptic partial differential equations of second order
• Multiplicity of positive solutions to a \(p\)-Laplacian equation involving critical nonlinearity.
• Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order
• Minimax theorems
• Positive solutions to a fourth-order elliptic problem by the Lusternik-Schnirelmann category
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Critical exponents and critical dimensions of polyharmonic operators
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
• A multiplicity result for a variational problem with lack of compactness
• A rellich type identity and applications
• Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik–Schnirelman theory
• Ground state and non-ground state solutions of some strongly coupled elliptic systems

This page was built for publication: Existence and multiplicity of positive solutions for a fourth-order elliptic equation