This paper is concerned with the following fractional Schrödinger equation {(-Δ)su+u=k(x)f(u)+h(x)inRNu∈Hs(RN),u>0inRN,where s∈ (0 , 1) , N> 2 s, (- Δ) s is the fractional Laplacian, k is a bounded positive function, h∈ L2(RN) , h≢ 0 is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that | h| 2 is sufficiently small.
Multiple Solutions for a Class of Nonhomogeneous Fractional Schrödinger Equations in RN
Ambrosio V.;
2018-01-01
Abstract
This paper is concerned with the following fractional Schrödinger equation {(-Δ)su+u=k(x)f(u)+h(x)inRNu∈Hs(RN),u>0inRN,where s∈ (0 , 1) , N> 2 s, (- Δ) s is the fractional Laplacian, k is a bounded positive function, h∈ L2(RN) , h≢ 0 is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that | h| 2 is sufficiently small.File in questo prodotto:
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