The Hadamard variational formula for the ground state value of \(- {\Delta{}}u={\lambda{}}|{}u|{}^{p-1}u\)

DOI10.2996/kmj/1138039602zbMath0825.35045OpenAlexW2081945789MaRDI QIDQ1209436

Tatsuzo Osawa

Publication date: 16 May 1993

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138039602

zbMATH Keywords

semilinear elliptic equationground state valueHadamarad variational formula

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Variational methods for higher-order elliptic equations (35J35)

Related Items (5)

Nonlinear eigenvalue problem and singular variation of domains ⋮ The Hadamard variation of the ground state value of some quasi-linear elliptic equations ⋮ Singular variation of nonlinear eigenvalues ⋮ Singular variation of the ground state eigenvalue for a semilinear elliptic equation ⋮ Homogenization of singular numbers for a non self-adjoint elliptic problem in a perforated domain.

Cites Work

• Unnamed Item
• Asymptotic property of an eigenfunction of the Laplacian under singular variation of domains - the Neumann condition -
• The effect of domain shape on the number of positive solutions of certain nonlinear equations
• Symmetry and related properties via the maximum principle
• The Hadamard variational formula for the Green functions of some normal elliptic boundary value problems
• Nonlinear eigenvalue problem and singular variation of domains
• Convexity of domain functionals
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents

This page was built for publication: The Hadamard variational formula for the ground state value of \(- {\Delta{}}u={\lambda{}}|{}u|{}^{p-1}u\)