A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
Copyright policy )A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
In this paper it is proved a critical point theorem of mountain-pass type which yields a sequence of critical points converging to zero. The proof combines a pseudo-gradient property with a deformation lemma. The abstract result is applied for proving a multiplicity result for the semilinear elliptic equation \(-\Delta u=f(x,u)\) in \(\Omega\) under the Dirichlet boundary condition \(u=0\) on \(\partial\Omega\), where \(\Omega\) is a bounded domain in \(\mathbb R^n\) with a smooth boundary and \(f(x,u)\) behaves like \(a(x)| u| ^p\)sgn\(\, u\) with \(0
Variational method, Symmetric mountain pass lemma, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, symmetric mountain pass lemma, Nonlinear elliptic equations, variational method, critical point theorem, Existence of solutions for minimax problems, Semilinear elliptic equation, Critical point theorem, semilinear elliptic equation, Analysis
Variational method, Symmetric mountain pass lemma, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, symmetric mountain pass lemma, Nonlinear elliptic equations, variational method, critical point theorem, Existence of solutions for minimax problems, Semilinear elliptic equation, Critical point theorem, semilinear elliptic equation, Analysis
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