Twin positive solutions for p-Laplacian nonlinear Neumann problems via variational and degree theoretic methods

Donal O'Regan

Twin positive solutions for p-Laplacian nonlinear Neumann problems via variational and degree theoretic methods

Mathematics

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Abstract

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). Using a combination of variational and degree theoretic techniques, we show that the problem has two positive smooth solutions. We also show the equivalence of W-n(1,p) and C-n(1) minimizers for a large class of locally Lipschitz functionals.

Original language	English (Ireland)
Number of pages	23
Journal	Journal Of Nonlinear And Convex Analysis
Volume	9
Publication status	Published - 1 Aug 2008

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Agarwal, R.P., Filippakis, M., Papageorgiou, N.S.

Cite this

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abstract = "We consider a nonlinear Neumann problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). Using a combination of variational and degree theoretic techniques, we show that the problem has two positive smooth solutions. We also show the equivalence of W-n(1,p) and C-n(1) minimizers for a large class of locally Lipschitz functionals.",

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AB - We consider a nonlinear Neumann problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). Using a combination of variational and degree theoretic techniques, we show that the problem has two positive smooth solutions. We also show the equivalence of W-n(1,p) and C-n(1) minimizers for a large class of locally Lipschitz functionals.

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JO - Journal Of Nonlinear And Convex Analysis

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ER -

Twin positive solutions for p-Laplacian nonlinear Neumann problems via variational and degree theoretic methods

Abstract

Authors (Note for portal: view the doc link for the full list of authors)

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Cite this