20.500.12556/RUL-111174 Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials This 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. fractional Schrödinger equations critical Sobolev exponent Ambrosetti-Rabinowitz condition concentration compactness principle true false true Angleški jezik Ni določen Članek v reviji 2019-09-25 14:17:19 2019-09-25 14:17:21 2022-08-23 03:41:20 0000-00-00 00:00:00 2016 0 0 Str. 48-68 Vol. 142 2016 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.95 0362-546X http://dx.doi.org/10.1016/j.na.2016.04.012 17674585 26027520 RAZ_Zhang_Xia_i2016.pdf RAZ_Zhang_Xia_i2016.pdf 1 562A99AD16437E80D267F150481F107B 1920756556f5581bac488e65468054cc776230684b26dd3b28354a194fccd0d3 52e28772-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=122997 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0