ALL libraries (COBIB.SI union bibliographic/catalogue database)
PDF
  • Multiplicity and concentration results for a ▫$(p, q)$▫-Laplacian problem in ▫${\mathbb{R}}^N$▫
    Ambrosio, Vincenzo, 1986- ; Repovš, Dušan, 1954-
    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$▫.
    Source: Zeitschrift für angewandte Mathematik und Physik. - ISSN 0044-2275 (Vol. 72, iss. 1, Feb. 2021, art. 33 (33 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2021
    Language - english
    COBISS.SI-ID - 47945731

    Link(s):

    https://doi.org/10.1007/s00033-020-01466-7
    Repository of the University of Ljubljana – RUL
    DOI

Shelf entry