Multiplicity and concentration results for a ▫$(p, q)$▫-Laplacian problem in ▫${\mathbb{R}}^N$▫Ambrosio, Vincenzo (Avtor) Repovš, Dušan (Avtor) (pq)-Laplacian problempositive solutionsvariational methodsLjusternik-Schnirelmann theoryIn 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$▫.20212021-01-25 07:52:23Članek v reviji124471sl