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The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems − div ( ϵ 2 ϕ ( ϵ | ∇ u | ) ∇ u ) + V ( x ) ϕ ( | u | ) u = f ( u ) in R N , $$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon|\nabla u|\bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$ where ϵ $\epsilon$ is a positive parameter, N ≥ 2 $N\geq2$ , V $V$ , f $f$ are continuous functions satisfying some technical conditions and ϕ $\phi$ is a C 1 $C^{1}$ -function.
Acta Applicandae Mathematicae – Springer Journals
Published: Jun 14, 2017
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