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arXiv · 1704.02477

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

Yavdat Il'yasov·Kaye Silva
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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 $\lambda^*$, 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 $\lambda^*$ is obtained.

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Yavdat Il'yasov, Kaye Silva. 2017-04-08. On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method. https://doi.org/10.1090/proc/13972

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