Nonlinear Neumann problems driven by a nonhomogeneous differential operator

Giovanni Molica Bisci; Dušan Repovš

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arXiv · 1608.07430

Nonlinear Neumann problems driven by a nonhomogeneous differential operator

Giovanni Molica Bisci·Dušan Repovš

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Abstract

We study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator $\operatorname{div}(a(x,\nabla u))$, a special case of which is the $p$-Laplacian. The reaction term is a nonlinearity function $f$ which exhibits $(p-1)$-subcritical growth. By using variational methods, we prove a multiplicity result on the existence of weak solutions for such problems. An explicit example of an application is also presented.

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Giovanni Molica Bisci, Dušan Repovš. 2016-08-26. Nonlinear Neumann problems driven by a nonhomogeneous differential operator. https://arxiv.org/abs/1608.07430

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