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Publicly Available Published by De Gruyter March 10, 2016

Multiplicity of Solutions For a Convex-concave Problem With a Nonlinear Boundary Condition

  • Emerson A.M. Abreu , Paulo C. Carrião and Olímpio H. Miyagaki

Abstract

We study the existence of multiple positive solutions for a convex-concave problem, denoted by (Pλμ), with a nonlinear boundary condition involving two critical exponents and two positive parameters λ and μ. We obtain a continuous strictly decreasing function f such that K1 ≡ {(f(μ), μ) : μ ∈ [0, ∞)} divides [0, ∞) × [0, ∞) \ {(0, 0)} in two connected sets K0 and K2 such that problem (Pλμ) has at least two solutions for (λ, μ) ∈ K2, at least one solution for (λ, μ) ∈ K1 and no solution for (λ, μ) ∈ K0.

Received: 2005-11-04
Published Online: 2016-03-10
Published in Print: 2006-02-01

© 2016 by Advanced Nonlinear Studies, Inc.

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