Multiplicity of Nontrivial Solutions of Semilinear Elliptic Equations
Copyright policy )Multiplicity of Nontrivial Solutions of Semilinear Elliptic Equations
It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser. 120, 113-137 (1979; Zbl 0426.35038)] as well as from \textit{N. Hirano} and \textit{T. Nishimura} [J. Math. Anal. Appl. 180, No. 2, 566-586 (1993; Zbl 0835.35052)].
- Southeast University China (People's Republic of)
Applied Mathematics, critical point, nontrivial solution, Dirichlet boundary value problem, Boundary value problems for second-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, reduction method, Sobolev's embedding theorem, semilinear elliptic equation, (PS) condition, Analysis, Critical points of functionals in context of PDEs (e.g., energy functionals)
Applied Mathematics, critical point, nontrivial solution, Dirichlet boundary value problem, Boundary value problems for second-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, reduction method, Sobolev's embedding theorem, semilinear elliptic equation, (PS) condition, Analysis, Critical points of functionals in context of PDEs (e.g., energy functionals)
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