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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.