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

Abstract

This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, the indefinite nonlinearity, and depend on the real parameter $\lambda$. A special focus is made on the extreme value of Nehari manifold ${\lambda }^{\ast }$, which determines the threshold of applicability of Nehari manifold method. In the main result the existence of two branches of positive solutions for the cases where parameter $\lambda$ lies above the threshold ${\lambda }^{\ast }$ is obtained.

14 pages

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