Multiple nontrivial solutions for a class of biharmonic elliptic equations with Sobolev critical exponent

DOI10.1155/2018/8212785zbMath1427.35032OpenAlexW2901095223MaRDI QIDQ1721495

Jun Wang, Maochun Zhu, Xiao Yong Qian

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/8212785

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40) Critical exponents in context of PDEs (35B33) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

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Cites Work

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• Superlinear critical resonant problems with small forcing term
• Semilinear elliptic equations for beginners. Existence results via the variational approach
• Existence of positive solutions of the equation \(-\Delta u+a(x)u=u^{(N+2)/(N-2)}\) in \({\mathbb{R}}^ N\)
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• The cubic fourth-order Schrödinger equation
• Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• 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
• Positive solutions in semilinear critical problems for polyharmonic operators
• Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order
• Minimax theorems
• A quasilinear elliptic problem involving critical Sobolev exponents
• A critical elliptic problem for polyharmonic operators
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Self-Focusing with Fourth-Order Dispersion
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• The existence of a positive solution of semilinear elliptic equations with limiting Sobolev exponent
• A rellich type identity and applications
• Positive solutions of a fourth-order semilinear problem involving critical growth
• Multiple solutions of a critical polyharmonic equation
• Non-trivial solutions for a semilinear biharmonic problem with critical growth and potential vanishing at infinity
• Singular Solutions of the Biharmonic Nonlinear Schrödinger Equation