Blow-up behavior of ground states of semilinear elliptic equations in \(R^ n\) involving critical Sobolev exponents

DOI10.1016/0022-0396(92)90136-BzbMath0761.35031OpenAlexW2090576571MaRDI QIDQ1194499

Xuefeng Wang, Xing-Bin Pan

Publication date: 27 September 1992

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

Full work available at URL: https://doi.org/10.1016/0022-0396(92)90136-b

zbMATH Keywords

entire solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Second-order elliptic equations (35J15)

Related Items (17)

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Cites Work

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• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• On isolated singularities of solutions of second order elliptic differential equations
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Uniqueness of non-negative solutions of semilinear equations in \({\mathbb{R}}^ n\)
• Elliptic equations with nearly critical growth
• Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Symmetry and related properties via the maximum principle
• On the existence of positive entire solutions of a semilinear elliptic equation
• On the existence and structure of stationary states for a nonlinear Klein-Gordon equation
• Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Emden-Fowler equations involving critical exponents
• On harnack type inequalities and their application to quasilinear elliptic equations

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