137 research outputs found
Multiple solutions for a class of nonhomogeneous fractional Schr\"odinger equations in
This paper is concerned with the following fractional Schr\"odinger equation
\begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^{s} u+u= k(x)f(u)+h(x)
\mbox{ in } \mathbb{R}^{N}\\ u\in H^{s}(\R^{N}), \, u>0 \mbox{ in }
\mathbb{R}^{N}, \end{array} \right. \end{equation*} where , , is the fractional Laplacian, is a bounded positive
function, , is nonnegative and
is either asymptotically linear or superlinear at infinity.\\ By using the
-harmonic extension technique and suitable variational methods, we prove the
existence of at least two positive solutions for the problem under
consideration, provided that is sufficiently small
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