caa a22 4500 605496021 CHVBK 20210128100534.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10231-014-0434-2 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0434-2 Multi-bump solutions for a class of quasilinear problems involving variable exponents [Elektronische Daten] [Claudianor Alves, Marcelo Ferreira] We establish the existence of multi-bump solutions for the following class of quasilinear problems $$\begin{aligned} - \Delta _{ p(x) } u + \big ( \lambda V(x) + Z(x) \big ) u ^{ p(x)-1 } = f(x,u) \text { in } \mathbb R^N, \, u \ge 0 \text { in } \mathbb R^N, \end{aligned}$$ - Δ p ( x ) u + ( λ V ( x ) + Z ( x ) ) u p ( x ) - 1 = f ( x , u ) in R N , u ≥ 0 in R N , where the nonlinearity $$ f :\mathbb R^N \times \mathbb R \rightarrow \mathbb R $$ f : R N × R → R is a continuous function having a subcritical growth and potentials $$ V, Z :\mathbb R^N \rightarrow \mathbb R $$ V , Z : R N → R are continuous functions verifying some hypotheses. The main tool used is the variational method. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Variational Methods nationallicence Positive solutions nationallicence Asymptotic behavior of solutions nationallicence $$p(x)$$ p ( x ) -Laplacian nationallicence Alves Claudianor Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP: 58429-900, Campina Grande, PB, Brazil aut Ferreira Marcelo Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP: 58429-900, Campina Grande, PB, Brazil aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1563-1593 0373-3114 194:6<1563 2015 194 10231 https://doi.org/10.1007/s10231-014-0434-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0434-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alves Claudianor Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP: 58429-900, Campina Grande, PB, Brazil aut NATIONALLICENCE 700 1- Ferreira Marcelo Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP: 58429-900, Campina Grande, PB, Brazil aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1563-1593 0373-3114 194:6<1563 2015 194 10231