ON BRANCHES OF POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS AT THE EXTREME VALUE OF THE NEHARI MANIFOLD METHOD.

This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, an indefinite nonlinearity, and depend on a real parameter λ. A special focus is given to the extreme value λ∗ of the Nehari manifold that determines the threshold of applicability of the Nehari manifold method. In the main result the existence of two branches of positive solutions for the cases where the parameter λ lies above the threshold λ∗ is obtained. [ABSTRACT FROM AUTHOR]