Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros

Guowei Dai

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arXiv · 1511.06756

Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros

Guowei Dai

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Abstract

In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem from infinity for nonlinear operator equation with homogeneous operator. To deal with the superlinear case, we establish several topological results involving superior limit.

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Guowei Dai. 2015-11-20. Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros. https://arxiv.org/abs/1511.06756

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