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.; Hajaiej, H.. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - 30:3(2018), pp. 1119-1143. [10.1007/s10884-017-9590-6]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
