The existence of three solutions for \(p\)-Laplacian problems with critical and supercritical growth

DOI10.1216/RMJ-2014-44-4-1383zbMath1350.35083MaRDI QIDQ470415

Lin Zhao, Pei-Hao Zhao

Publication date: 12 November 2014

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1414760960

zbMATH Keywords

variational methodscritical point theoryMoser iterationthree solutions

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Variational methods for higher-order elliptic equations (35J35)

Related Items (6)

Supercritical fractional Kirchhoff type problems ⋮ BOUNDED MULTIPLE SOLUTIONS FOR -LAPLACIAN PROBLEMS WITH ARBITRARY PERTURBATIONS ⋮ Multiple solutions for double phase problems in \(\mathbb{R}^n\) via Ricceri's principle ⋮ Soliton solutions for a singular Schrödinger equation with any growth exponents ⋮ (Super)critical nonlocal equations with periodic boundary conditions ⋮ Infinitely many radial solutions for a sub-super critical \(p\)-Laplacian problem

Cites Work

• Unnamed Item
• Unnamed Item
• Sobolev embeddings involving symmetry
• Positive solutions for some quasilinear equations with critical and supercritical growth
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Compact Sobolev embedding theorems involving symmetry and its application
• A three critical points theorem revisited
• A further three critical points theorem
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Existence theorems for elliptic equations involving supercritical Sobolev exponent
• Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
• Quasilinear elliptic equations involving critical Sobolev exponents
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
• On an elliptic equation of p-Kirchhoff type via variational methods
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• A multiplicity result for quasilinear elliptic equations involving critical sobolev exponents
• SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
• On the infinitely many positive solutions of a supercritical elliptic problem

This page was built for publication: The existence of three solutions for \(p\)-Laplacian problems with critical and supercritical growth