Existence and nonexistence results for critical growth polyharmonic elliptic systems

DOI10.1016/j.jde.2004.12.001zbMath1189.35083OpenAlexW1994660466MaRDI QIDQ2576910

Yuxia Guo, Thomas J. Bartsch

Publication date: 29 December 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.12.001

zbMATH Keywords

critical Sobolev exponentsvariational methodspolyharmonic elliptic system

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for elliptic systems (35J50) Higher-order elliptic systems (35J48) Boundary value problems for higher-order elliptic systems (35J58)

Related Items (15)

Least energy solutions for semilinear Schrödinger systems with electromagnetic fields and critical growth ⋮ Bounded positive entire solutions of singular quasilinear elliptic equations ⋮ Positive minimizers of the best constants and solutions to coupled critical quasilinear systems ⋮ Nontrivial solutions for critical potential elliptic systems ⋮ Elliptic system with some singular nonlinearity ⋮ Existence and multiplicity results for critical growth polyharmonic elliptic systems ⋮ Existence results and a priori bounds for higher order elliptic equations and systems ⋮ Factorization into \(k\)-bubbles for Palais-Smale maps to potential type energy functionals ⋮ Positive solutions of polyharmonic equations with strong dependence on the gradient ⋮ Multiple nontrivial solutions for critical growth quasilinear elliptic systems ⋮ Existence and nonexistence results for critical growth fractional elliptic systems ⋮ Existence and multiplicity of positive solutions for semilinear elliptic systems with Sobolev critical exponents ⋮ Optimal conditions for \(L^\infty \)-regularity and a priori estimates for semilinear elliptic systems ⋮ Critical polyharmonic systems and optimal partitions ⋮ On nontrivial solutions of critical polyharmonic elliptic systems

Cites Work

• The concentration-compactness principle in the calculus of variations. The limit case. I
• Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents
• 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
• Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order
• Critical exponents and critical dimensions of polyharmonic operators
• Critical exponents, critical dimensions and the biharmonic operator
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• The best sobolev constant
• Existence and regularity of weak solutions to the Dirichletproblem for semilinear elliptic systems of higher order.
• Strongly indefinite systems with critical Sobolev exponents
• Multiple solutions of a critical polyharmonic equation
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