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

Guowei  Dai

doi:10.3934/dcds.2016034

Article Contents

2016, Volume 36, Issue 10: 5323-5345. Doi: 10.3934/dcds.2016034

This issue Previous Article Partial regularity of solutions to the fractional Navier-Stokes equations Next Article Periodic and eventually periodic points of affine infra-nilmanifold endomorphisms

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

Guowei Dai^1,

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024

Received: March 31, 2015

Revised: March 31, 2016

Published: May 2017

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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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Mathematics Subject Classification: Primary: 47J15, 47J05; Secondary: 35J60, 35B40.

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