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June  2010, 28(2): 637-648. doi: 10.3934/dcds.2010.28.637

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

Cristian Bereanu 1, , Petru Jebelean 2, and  Jean Mawhin 3,

1. 

Institute of Mathematics "Simion Stoilow” of the Romanian Academy, 21, Calea Griviţei, RO-010702-Bucharest, Sector 1, Romania
2. 

Department of Mathematics, West University of Timişoara, 4, Blvd. V. Pârvan, RO-300223-Timişoara, Romania
3. 

Institute of Mathematics and Physics, Université Catholique de Louvain, 2, chemin du cyclotron, B-1348 Louvain-la-Neuve, Belgium

Received  January 2010 Revised  April 2010 Published  April 2010

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, Leray-Schauder degree, upper and lower solutions., pendulum-like nonlinearities.
Mathematics Subject Classification: Primary: 35J65; Secondary: 34B1.
Citation: Cristian Bereanu, Petru Jebelean, Jean Mawhin. Radial solutions for Neumann problems with $\phi$-Laplacians and pendulum-like nonlinearities. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 637-648. doi: 10.3934/dcds.2010.28.637
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