Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentialsZhang, Xia (Avtor)
Zhang, Binlin (Avtor)
Repovš, Dušan (Avtor)
fractional Schrödinger equationscritical Sobolev exponentAmbrosetti-Rabinowitz conditionconcentration compactness principleThis paper is concerned with the following fractional Schrödinger equations involving critical exponents: ▫$$(-\Delta)^\alpha u + V(x)u = k(x)f(u) + \lambda|u|^{2_\alpha^\ast-2}u \quad \text{in} \; \mathbb{R}^N,$$▫ where ▫$(-\Delta)^\alpha$▫ is the fractional Laplacian operator with ▫$\alpha \in (0,1)$▫, ▫$N \ge 2$▫, ▫$\lambda$▫ is a positive real parameter and ▫$2_\alpha^\ast = 2N/(N-2\alpha)$▫ is the critical Sobolev exponent, ▫$V(x)$▫ and ▫$k(x)$▫ are positive and bounded functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space and the minimax arguments, we obtain the existence of a nontrivial radially symmetric weak solution for the above-mentioned equations without assuming the Ambrosetti-Rabinowitz condition on the subcritical nonlinearity.20162019-09-25 14:17:19Članek v reviji111174sl