Radial solutions for Neumann problems with  $\phi$-Laplacians and pendulum-like nonlinearities

Cristian Bereanu; Petru Jebelean; Jean Mawhin

doi:10.3934/dcds.2010.28.637

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2010, Volume 28, Issue 2: 637-648. Doi: 10.3934/dcds.2010.28.637 open access

This issue Previous Article Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source Next Article Age-dependent equations with non-linear diffusion

Radial solutions for Neumann problems with $\phi$-Laplacians and pendulum-like nonlinearities

1.
Institute of Mathematics "Simion Stoilow” of the Romanian Academy, 21, Calea Griviţei, RO-010702-Bucharest, Sector 1
2.
Department of Mathematics, West University of Timişoara, 4, Blvd. V. Pârvan, RO-300223-Timişoara
3.
Institute of Mathematics and Physics, Université Catholique de Louvain, 2, chemin du cyclotron, B-1348 Louvain-la-Neuve

Received: December 31, 2009

Revised: March 31, 2010

Published: June 2010

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Abstract

In this paper we study the existence and multiplicity of radial solutions for Neumann problems in a ball and in an annular domain, associated to pendulum-like perturbations of mean curvature operators in Euclidean and Minkowski spaces and of the $p$-Laplacian operator. Our approach relies on the Leray-Schauder degree and the upper and lower solutions method.

Keywords:

mean curvature and $p$-Laplacian operators,
Neumann problem,
pendulum-like nonlinearities,
Leray-Schauder degree,
upper and lower solutions.

Mathematics Subject Classification: Primary: 35J65; Secondary: 34B15.

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Radial solutions for Neumann problems with $\phi$-Laplacians and pendulum-like nonlinearities

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