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- W2338181569 abstract "We study the existence, concentration and multiplicity of weak solutions to thequasilinear Schrödinger equation with critical Sobolev growthbegin{equation*}left{ begin{gathered} - {varepsilon ^2}Delta u + V(x)u - {varepsilon ^2}Delta (u^2)u = W(x){u^{q - 1}} + {u^{2cdot{2^*} - 1}} {text{ in }}{mathbb{R}^N},u > 0{text{ in }}{mathbb{R}^N},end{gathered} right.end{equation*}where $varepsilon $ is a small positive parameter, $N ge 3$, ${2^ * } = frac{{2N}}{{N - 2}}$, $4 0$ and $inf W > 0$. Under proper assumptions, we obtain the existence and concentration phenomena of soliton solutions of the above problem. With minimax theorems and Ljusternik-Schnirelmann theory, we also obtain multiple soliton solutions by employing the topology of the set where the potentials $V(x)$ attains its minimum and $W(x)$ attains its maximum." @default.
- W2338181569 created "2016-06-24" @default.
- W2338181569 creator A5002493025 @default.
- W2338181569 creator A5030766995 @default.
- W2338181569 date "2015-08-01" @default.
- W2338181569 modified "2023-09-25" @default.
- W2338181569 title "Concentrating soliton solutions for quasilinear Schrödinger equations involving critical Sobolev exponents" @default.
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- W2338181569 doi "https://doi.org/10.3934/dcds.2016.36.731" @default.
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