Non-homogeneous Dirichlet problems with concave-convex reaction

  • Gabriele Bonanno

    Università di Messina, Italy
  • Roberto Livrea

    University of Palermo, Italy
  • Vicenţiu D. Rădulescu

    AGH University, Kraków, Poland; University of Craiova; Romanian Academy, Bucharest, Romania
Non-homogeneous Dirichlet problems with concave-convex reaction cover

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Abstract

The variational methods are adopted for establishing the existence of at least two nontrivial solutions for a Dirichlet problem driven by a non-homogeneous differential operator of -Laplacian type. A large class of nonlinear terms is considered, covering the concave-convex case. In particular, two positive solutions to the problem are obtained under a -superlinear growth at infinity, provided that a behaviour less than -linear of the nonlinear term in a suitable set is requested.

Cite this article

Gabriele Bonanno, Roberto Livrea, Vicenţiu D. Rădulescu, Non-homogeneous Dirichlet problems with concave-convex reaction. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 4, pp. 799–818

DOI 10.4171/RLM/959