Local minimizers over the Nehari manifold for a class of concave-convex problems with sign changing nonlinearity

Abstract

We study a $p$-Laplacian equation involving a parameter $\lambda$ and a concave-convex nonlinearity containing a weight which can change sign. By using the Nehari manifold and the fibering method, we show the existence of two positive solutions on some interval $(0,{\lambda }^{\ast }+\epsilon )$, where ${\lambda }^{\ast }$ can be characterized variationally. We also study the asymptotic behavior of solutions when $\lambda \downarrow 0$.

References in corpus (1)

• On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method

Cited by in corpus (4)

• The bifurcation diagram of an elliptic Kirchhoff-type equation with respect to the stiffness of the material
• Multiplicity of negative-energy solutions for singular-superlinear Schrödinger equations with indefinite-sign potential
• On The Extremal Parameters Curve of a Quasilinear Elliptic System of Differential Equations
• On subhomogeneous indefinite $p$-Laplace equations in supercritical spectral interval