Existence and multiplicity of positive solutions for a class of nonlinear elliptic problems

Authors: ASADOLLAH AGHAJANI, JAMILE SHAMSHIRI, FRAJOLLAH MOHAMMADI YAGHOOBI

Abstract: We study the existence and multiplicity of nonnegative solutions for the nonlinear elliptic problem, -\Delta u+v(x)u=a(x)u^p+\lambda f(x,u) for x\in\Omega and u=0 on \partial\Omega, where \Omega is a bounded region in R^N, N>2, 10 and f(x,u) satisfies some suitable conditions. By extracting the Palais-Smale sequences in the Nehari manifold, it is proved that there exists \lambda^* such that for \lambda \in (0,\lambda^*), the above problem has at least two positive solutions.

Keywords: Nehari manifold, critical point, nonlinear elliptic boundary value problem, Palais-Smale sequence

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