20.500.12556/RUL-132481 The behavior of solutions of a parametric weighted (p,q)-Laplacian equation We study the behavior of solutions for the parametric equation ▫$$-\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z) = \lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda >0,$$▫ under Dirichlet condition, where ▫$\Omega \subseteq \mathbb{R}^N$▫ is a bounded domain with a ▫$C^2$▫-boundary ▫$\partial \Omega$▫, ▫$a_1, a_2 \in L^\infty(\Omega)$▫ with ▫$a_1(z), a_2(z) > 0$▫ for a.a. ▫$z \in \Omega$▫, ▫$p, q \in (1, \infty)$▫ and ▫$\Delta_{p}^{a_1}$▫, ▫$\Delta_{q}^{a_2}$▫ are weighted versions of ▫$p$▫-Laplacian and ▫$q$▫-Laplacian. We prove existence and nonexistence of nontrivial solutions, when ▫$f(z,x)$▫ asymptotically as ▫$x \to \pm \infty$▫ can be resonant. In the studied cases, we adopt a variational approach and use truncation and comparison techniques. When ▫$\lambda$▫ is large, we establish the existence of at least three nontrivial smooth solutions with sign information and ordered. Moreover, the critical parameter value is determined in terms of the spectrum of one of the differential operators. weighted (p q)-Laplacian resonant Carathéodory function parametric power term positive and negative solutions nodal solutions true false false Angleški jezik Ni določen Članek v reviji 2021-10-27 10:37:58 2021-10-27 10:38:02 2022-09-12 04:12:36 0000-00-00 00:00:00 2022 0 0 Str. 499-517 Iss. 1 Vol. 7 2022 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 2473-6988 10.3934/math.2022032 81064195 RAZ_Repovs_Dusan_2022.pdf RAZ_Repovs_Dusan_2022.pdf 1 2F540C4A142EF2FD5619128B2744886D 046df2df50a41555eda66444eb52db82579afd766001791d6abdd75131ed6a27 0280b135-3702-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=150129 https://www.aimspress.com/article/doi/10.3934/math.2022032 0 2230c5e3-3702-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=150130 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0