Some results for semilinear differential equations at resonance
The author considers the problem of the existence of a solution of a so- called resonance problem that is, for an equation of the type \[ (1)\quad Au=F(x,u)\quad in\quad \Omega, \] where the linear (differential) operator A is self-adjoint with a nontrivial kernel on \(L_ 2(\Omega)\) and the nonlinear map F(x,\(\xi)\) satisfies some growth conditions for large values of \(| \xi |\). This paper is written in the spirit of the approach of the paper of \textit{E. M. Landesman} and \textit{A. C. Lazer}, J. Math. Mech. 19, 609-623 (1970; Zbl 0193.392).
semilinear differential equations at resonance
scientific article; zbMATH DE number 3842560