Tohoku Mathematical Journal
2014
March
SECOND SERIES VOL. 66, NO. 1

Tohoku Math. J.
66 (2014), 137-153

Title EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS FOR PARAMETRIC NEUMANN PROBLEMS WITH $p$-LAPLACIAN

Author Dumitru Motreanu, V. V. Motreanu and N. S. Papageorgiou

(Received July 2, 2012)
Abstract. Using variational methods based on the critical point theory and suitable truncation and comparison techniques, we study existence, multiplicity and nonexistence of positive solutions for a parametric nonlinear Neumann problem driven by the $p$-Laplacian. Our hypotheses cover the case of nonlinearities of concave-convex type whose exponents depend on the parameter.

Mathematics Subject Classification. Primary 35J25; Secondary 35J92.
Key words and phrases. $p$-Laplacian, concave-convex nonlinearities, positive solutions, bifurcation-type theorem.

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