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

Guowei Dai | Zendy

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

Author(s) -

Guowei Dai

Publication year - 2016

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2016034

Subject(s) - bifurcation , mathematics , multiplicity (mathematics) , nonlinear system , mathematical analysis , bifurcation theory , laplace operator , operator (biology) , sign (mathematics) , p laplacian , limit (mathematics) , infinity , pure mathematics , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , boundary value problem

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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