20.500.12556/RUL-124471 Multiplicity and concentration results for a ▫$(p, q)$▫-Laplacian problem in ▫${\mathbb{R}}^N$▫ In this paper, we study the multiplicity and concentration of positive solutions for the following ▫$(p, q)$▫-Laplacian problem: ▫$$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{p} u -\Delta _{q} u +V(\varepsilon x) \left( |u|^{p-2}u + |u|^{q-2}u\right) = f(u) &{} \text{ in } {\mathbb{R}}^{N}, \\ u\in W^{1, p}({\mathbb{R}}^{N})\cap W^{1, q}({\mathbb{R}}^{N}), \quad u>0 \text{ in } {\mathbb{R}}^{N}, \end{array} \right. \end{aligned}$$▫ where ▫$\varepsilon >0$▫ is a small parameter, ▫$1 < p < q < N$▫, ▫$ \Delta _{r}u={{\,\mathrm{div}\,}}(|\nabla u|^{r-2}\nabla u)$▫, with ▫$r\in \{p, q\}$▫, is the ▫$r$▫-Laplacian operator, ▫$V:{\mathbb{R}}^{N}\rightarrow {\mathbb{R}}$▫ is a continuous function satisfying the global Rabinowitz condition, and ▫$f:{\mathbb{R}}\rightarrow {\mathbb{R}}$▫ is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik-Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where ▫$V$▫ attains its minimum for small ▫$\varepsilon$▫. (p q)-Laplacian problem positive solutions variational methods Ljusternik-Schnirelmann theory true false true Angleški jezik Ni določen Članek v reviji 2021-01-25 07:52:23 2021-01-25 07:52:27 2022-09-04 03:59:39 0000-00-00 00:00:00 2021 0 0 art. 33 (33 str.) iss. 1 Vol. 72 Feb. 2021 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2021-07-01 517.956 0044-2275 10.1007/s00033-020-01466-7 47945731 26662656 RAZ_Ambrosio_Vincenzo_2021.pdf RAZ_Ambrosio_Vincenzo_2021.pdf 1 192A534A34260DC7CD902D1E1E1BAF45 55d7696cb3355d0a7c9e76580120ebd71c4cfc47cc27af3537a1161f0def1ff0 9e4500ab-e875-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=145314 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0