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- W2964287625 abstract "Abstract In this paper, we deal with the singular perturbed fractional elliptic problem <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mrow> <m:mi>ε</m:mi> <m:mo></m:mo> <m:msup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo>-</m:mo> <m:mi mathvariant=normal>Δ</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>V</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>z</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi>f</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>u</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> $varepsilon(-Delta)^{1/2}{u}+V(z)u=f(u)$ in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>ℝ</m:mi> </m:math> $mathbb{R}$ , where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:mo>-</m:mo> <m:mi mathvariant=normal>Δ</m:mi> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mo></m:mo> <m:mi>u</m:mi> </m:mrow> </m:math> ${(-Delta)^{1/2}u}$ is the square root of the Laplacian and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>f</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>s</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> ${f(s)}$ has exponential critical growth. Under suitable conditions on <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>f</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>s</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> ${f(s)}$ , we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of V as ε goes to 0." @default.
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- W2964287625 date "2016-10-11" @default.
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- W2964287625 title "Concentration Phenomena for Fractional Elliptic Equations Involving Exponential Critical Growth" @default.
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