Asymptotic behavior of solutions of a biharmonic Dirichlet problem with large exponents

DOI10.1007/s11854-011-0021-zzbMath1314.35059OpenAlexW2013843520MaRDI QIDQ2342970

Sanjiban Santra, Wei, Juncheng

Publication date: 30 April 2015

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-011-0021-z

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Higher-order elliptic equations (35J30) Semilinear elliptic equations (35J61) Green's functions for elliptic equations (35J08) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (5)

Asymptotic behavior of least energy solutions to the Finsler Lane-Emden problem with large exponents ⋮ Asymptotic behavior of sign-changing radial solutions of a semilinear elliptic equation in \(\mathbb{R}^2\) when exponent approaches \(+\infty\) ⋮ Blow up solutions for 4-dimensional elliptic problems involving exponentially dominated nonlinearities ⋮ Asymptotic behavior of least energy nodal solutions for biharmonic Lane-Emden problems in dimension four ⋮ Asymptotic profile of positive solutions of Lane-Emden problems in dimension two

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimates for Green function and Poisson kernels of higher-order Dirichlet boundary value problems
• A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
• Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions
• A sharp inequality of J. Moser for higher order derivatives
• Mean value formulas, Weyl's lemma and Liouville theorems for \(\Delta^ 2\) and Stokes' system
• Classification of solutions of higher order conformally invariant equations
• A sup+inf inequality for some nonlinear elliptic equations involving exponential nonlinearities
• Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Global compactness properties of semilinear elliptic equations with critical exponential growth
• Best constant for the embedding of the space \(H^ 2\cap H^ 1_ 0(\Omega)\) into \(L^{2N/(N-4)}\Omega\)
• Single-point condensation phenomena for a four-dimensional biharmonic Ren-Wei problem
• Singular limits in Liouville-type equations
• Existence of conformal metrics with constant \(Q\)-curvature
• Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity
• Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent
• Concentration phenomena for Liouville's equation in dimension four
• Asymptotic behavior of least energy solutions to a four-dimensional biharmonic semilinear problem
• Asymptotic Behavior of Least Energy Solutions of a Biharmonic Equation in Dimension Four
• Radial symmetry of positive solutions to nonlinear polyharmonic Dirichlet problems
• Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition
• Differential operators cononically associated to a conformal structure.
• A rellich type identity and applications
• On a Two-Dimensional Elliptic Problem with Large Exponent in Nonlinearity
• Locating the peaks of solutions via the maximum principle II: A local version of the method of moving planes
• Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity
• Single-point condensation and least-energy solutions
• Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients

This page was built for publication: Asymptotic behavior of solutions of a biharmonic Dirichlet problem with large exponents