On a class of fractional Laplacian problems with variable exponents and indefinite weights

• Autores: Nguyen Thanh Chung, Hoang Quoc Toan
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 2, 2020, págs. 223-237
• Idioma: inglés
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• Resumen

  • Let \Omega \subset {\mathbb {R}}^N, N\ge 2, be a bounded smooth domain. In this paper, we consider a class of fractional Laplacian problems of the form \begin{aligned} \left\{ \begin{array}{ll} (\Delta )^s_{p_1(x,.)}u(x)+(\Delta )^s_{p_2(x,.)}u(x) + |u|^{q(x)-2}u = \lambda V_1(x)|u(x)|^{r_1(x)-2}u(x) \\ \qquad - \mu V_2(x)|u(x)|^{r_2(x)-2}u(x) \hbox { in }\Omega , \\ u(x) = 0 \; \hbox { in } \partial \Omega , \end{array} \right. \end{aligned} where (\Delta )^s_{p_i(.,.)} (0