Multiple positive solutions for an elliptic problem involving a critical Sobolev exponent

DOI10.1080/00036811.2021.1889524zbMath1498.35305OpenAlexW3133181869MaRDI QIDQ5867318

Zhiyong Wang, Pei Ma, Tiantian Zheng, Ji Hui Zhang

Publication date: 14 September 2022

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2021.1889524

zbMATH Keywords

existencevariational methodscritical Sobolev exponentsemilinear equation with Laplacian

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items

Existence and multiplicity of positive solutions for a class of critical fractional Laplacian systems

Cites Work

• Unnamed Item
• The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent
• Positive solutions for nonhomogeneous elliptic equations involving critical Sobolev exponent
• Multiple positive solutions for semilinear elliptic systems
• Multiplicity of positive solutions for a critical quasilinear elliptic system with concave and convex nonlinearities
• Multiple positive solutions for Kirchhoff-type problems in \({\mathbb{R}^3}\) involving critical Sobolev exponents
• Existence and multiplicity of solutions for a class of elliptic problem with critical growth
• Existence of positive solutions of the equation \(-\Delta u+a(x)u=u^{(N+2)/(N-2)}\) in \({\mathbb{R}}^ N\)
• Multiple positive solutions for a critical quasilinear elliptic system with concave-convex nonlinearities
• Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Multiplicity of positive solutions for a class of concave-convex elliptic equations with critical growth
• Multiplicity of positive solutions to a \(p\)-Laplacian equation involving critical nonlinearity.
• Positive solutions of a Schrödinger equation with critical nonlinearity
• Multiplicity results for some nonlinear elliptic equations
• Minimax theorems
• Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity
• Dual variational methods in critical point theory and applications
• Regularity for minimizers for functionals of double phase with variable exponents
• Multiple positive solutions for a class of Kirchhoff type problems involving critical Sobolev exponents
• The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions
• Multiple positive solutions for a critical elliptic system with concave and convex nonlinearities
• Multiple positive solutions for indefinite semilinear elliptic problems involving a critical Sobolev exponent
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On an Elliptic Equation with Concave and Convex Nonlinearities
• Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝ^N
• Existence of solutions for a critical (p₁(x), … , p_n(x))-Kirchhoff-type potential systems
• Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight
• PARTIAL REGULARITY OF THE MINIMIZERS OF QUADRATIC FUNCTIONALS WITH VMO COEFFICIENTS