Constant sign and nodal solutions for anisotropic eigenvalue problems

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2025年7月3日

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Eylem Öztürk,
Nikolaos S. Papageorgiou

摘要

We consider a nonlinear eigenvalue problem driven by the anisotropic (p, q)-Laplacian. Using variational tools, truncations, comparisons and critical groups, we show that for all small values of the parameter, the problem has extremal constant sign solutions and nodal solutions. These solutions are ordered and vanish in $C_0^1(\overline{\Omega })$ $C_{0}^{1} (\bar{Ω})$ as $\lambda \rightarrow 0^+$ $λ \to 0^{+}$ .