A critical elliptic problem for polyharmonic operators
From MaRDI portal
Publication:2429764
DOI10.1016/j.jfa.2011.01.005zbMath1216.35074OpenAlexW2013047946MaRDI QIDQ2429764
Feng Zhou, Yuxin Ge, Wei, Juncheng
Publication date: 4 April 2011
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2011.01.005
Boundary value problems for higher-order elliptic equations (35J40) Geometric theory, characteristics, transformations in context of PDEs (35A30) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)
Related Items (12)
Polyharmonic Kirchhoff type equations with singular exponential nonlinearities ⋮ On the ground state solution for a critical fractional Laplacian equation ⋮ On an elliptic Kirchhoff–Boussinesq type problems with exponential growth ⋮ Multiple nontrivial solutions for a class of biharmonic elliptic equations with Sobolev critical exponent ⋮ Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights ⋮ Existence and multiplicity results for critical growth polyharmonic elliptic systems ⋮ Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik–Schnirelman theory ⋮ Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary ⋮ GJMS-type operators on a compact Riemannian manifold: best constants and Coron-type solutions ⋮ Nodal solutions for elliptic equation involving the GJMS operators on compact manifolds ⋮ Multiple solutions to polyharmonic elliptic problem involving GJMS operator on compact manifolds ⋮ Existence results for superlinear elliptic equations with nonlinear boundary value conditions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Ground state solutions for a semilinear problem with critical exponent.
- Periodic nonlinear Schrödinger equation with application to photonic crystals
- The concentration-compactness principle in the calculus of variations. The limit case. II
- On the Brézis-Nirenberg problem
- A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
- Ground state solutions for some indefinite variational problems
- Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
- An existence result for nonliner elliptic problems involving critical Sobolev exponent
- Best constant in Sobolev inequality
- Classification of solutions of higher order conformally invariant equations
- Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents
- Sharp Sobolev inequalities in critical dimensions.
- Concentration estimates and multiple solutions to elliptic problems at critical growth
- Existence and nonexistence results for critical growth biharmonic elliptic equations
- A Sobolev inequality with remainder term and critical equations on domains with topology for the polyharmonic operator
- Positive solutions in semilinear critical problems for polyharmonic operators
- On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent
- Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order
- Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
- Solutions with multiple spike patterns for an elliptic system
- Multiple solutions for the Brezis-Nirenberg problem
- Critical exponents and critical dimensions of polyharmonic operators
- Critical exponents, critical dimensions and the biharmonic operator
- Unique Continuation for Elliptic Equations
- On a Class of Nonlinear Second-Order Differential Equations
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- The best sobolev constant
- Strong unique continuation for 𝑚-th powers of a Laplacian operator with singular coefficients
- On multiple solutions of △u+λu+|u|4(n−2)u = 0
- Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains
- Critical growth problems for polyharmonic operators
- Critical semilinear biharmonic equations in RN
- A rellich type identity and applications
- Estimations of the best constant involving the L2norm in Wente's inequality and compact H-surfaces in Euclidean space
- A MULTIPLICITY RESULT FOR ELLIPTIC EQUATIONS AT CRITICAL GROWTH IN LOW DIMENSION
- ON THE ROLE OF SPACE DIMENSION [xxx IN THE SEMILINEAR BREZIS-NIRENBERG EIGENVALUE PROBLEM]
- ON A CONJECTURE OF P. PUCCI AND J. SERRIN
- Critical dimensions and higher order Sobolev inequalities with remainder terms
This page was built for publication: A critical elliptic problem for polyharmonic operators
