Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu, Anisotropic (p,q)-equations with a locally defined reaction

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DOI: 10.23952/asvao.6.2024.1.06
Volume 6, Issue 1, 1 April 2024, Pages 65-80

Abstract. We consider a nonlinear Dirichlet problem driven by the anisotropic $(p,q)$ -Laplacian, and a Carathéodory reaction $f(z,x)$ ( $z\in\Omega\subseteq\mathbb{R}^{N},$ $x\in\mathbb{R}$ ), which is only locally defined around zero in $x\in\mathbb{R}$ . We prove a mltiplicity theorem providing sign information for all the solutions, which are also ordered. Also, under a symmetry condition on $f(z,\cdot),$ we generate a whole sequence of nodal smooth solutions, converging to zero in $C_{0}^{1}(\overline{\Omega}).$

How to Cite this Article:
S. Aizicovici, N. S. Papageorgiou, V. Staicu, Anisotropic (p,q)-equations with a locally defined reaction, Appl. Set-Valued Anal. Optim. 6 (2024), 65-80.