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• W2003142972 abstract "We consider the following perturbed version of quasilinear Schrödinger equation $$begin{array}{lll}-varepsilon^2Delta u +V(x)u-varepsilon^2Delta (u^2)u=h(x,u)u+K(x)|u|^{22^*-2}uend{array}$$ in $${mathbb{R}^N}$$ , where N ≥ 3, 22* = 4N/(N − 2), V(x) is a nonnegative potential, and K(x) is a bounded positive function. Using minimax methods, we show that this equation has at least one positive solution provided that $${varepsilon leq mathcal{E}}$$ ; for any $${minmathbb{N}}$$ , it has m pairs of solutions if $${varepsilon leq mathcal{E}_m}$$ , where $${mathcal{E}}$$ and $${mathcal{E}_m}$$ are sufficiently small positive numbers. Moreover, these solutions $${u_varepsilon to 0}$$ in $${H^1(mathbb{R}^N)}$$ as $${varepsilon to 0}$$ ." @default.
• W2003142972 created "2016-06-24" @default.
• W2003142972 creator A5008600493 @default.
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• W2003142972 date "2012-01-06" @default.
• W2003142972 modified "2023-10-03" @default.
• W2003142972 title "Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in $${mathbb{R}^N}$$" @default.
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• W2003142972 doi "https://doi.org/10.1007/s10231-011-0246-6" @default.
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