20.500.12556/RUL-182455 The Nehari manifold approach for singular equations involving the $p(x)$-Laplace operator We study the following singular problem involving the $p(x)$-Laplace operator $\Delta p(x)u = \mathrm{div}(|\nabla u|^{p(x)-2} \nabla u)$, where $p(x)$ is a nonconstant continuous function $$ (P_\lambda) \quad \begin{cases} -\Delta_{p(x)}u = a(x)|u|^{q(x)-2}u(x) + \frac{\lambda b(x)}{u^{\delta(x)}} & \text{in} \; \Omega, \\ u>0 & \text{in} \; \Omega, \\ u=0 &\text{on} \; \partial\Omega. \end{cases} $$ Here, $\Omega$ is a bounded domain in $\mathbb{R}^{N \ge 2}$ with $C^2$-boundary, $\lambda$ is a positive parameter, $a(x), b(x) \in C(\overline{\Omega})$ are positive weight functions with compact support in $\Omega$, and $\delta(x), p(x), q(x) \in C(\overline{\Omega})$ satisfy certain hypotheses $(A_0)$ and $(A_1)$. We apply the Nehari manifold approach and some new techniques to establish the multiplicity of positive solutions for problem $(P_\lambda)$. Nehari manifold generalized Lebesgue-Sobolev space topological method singular equation p(x)-Laplace operator multiplicity true false true Angleški jezik Angleški jezik Članek v reviji 2026-05-12 12:02:57 2026-05-12 12:03:00 2026-05-13 04:51:35 0000-00-00 00:00:00 2023 0 0 Str. 135-149 no. 1 Vol. 68 2023 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 517.956 1747-6933 10.1080/17476933.2021.1980878 80237571 COBISS-ID_80237571.pdf COBISS-ID_80237571.pdf 1 60586251B05F1F608408F362AB4BF64E a3fbded43a0bb436854cf265da5f5ad7a4e69fb160742ca42ccf27dc43ed0bc9 b405ac9a-4de9-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233730 https://www.tandfonline.com/doi/full/10.1080/17476933.2021.1980878 1 76c8f96a-4de9-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233729 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0