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arXiv · 1812.08055

On a Dirichlet problem with $(p,q)$-Laplacian and parametric concave-convex nonlinearity

Salvatore A. Marano·Greta Marino·Nikolaos S. Papageorgiou
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Abstract

A homogeneous Dirichlet problem with $(p,q)$-Laplace differential operator and reaction given by a parametric $p$-convex term plus a $q$-concave one is investigated. A bifurcation-type result, describing changes in the set of positive solutions as the parameter $λ>0$ varies, is proven. Since for every admissible $λ$ the problem has a smallest positive solution $\bar u_λ$, both monotonicity and continuity of the map $ λ\mapsto \bar u_λ$ are studied.

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Salvatore A. Marano, Greta Marino, Nikolaos S. Papageorgiou. 2018-12-19. On a Dirichlet problem with $(p,q)$-Laplacian and parametric concave-convex nonlinearity. https://arxiv.org/abs/1812.08055

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