Cabre X., Sire Y., Nonlinear equations for fractional Laplacians II: existence, uniqueness, and qualitative properties of solutions. Trans. Am. Math. Soc. 367 (2015), no. 2, 911-941.Cabré, X., Sire, Y.: Nonlinear equations for fractional Laplacians II: existence, uniqueness, and ...
In this paper, we deal with a class of nonlinear fractional Choquard equations with indefinite potential (−Δ)αu+V(x)u=[∫RNM(ϵy)G(u)|x−y|μdy]M(ϵx)g(u),x∈RN, (1.1) whereϵ>0is a parameter,α∈(0,1),N>2α,(−Δ)αstands for the fractional Laplacian operat...
Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian Proc. Roy. Soc. Edinburgh Sect. A, 142 (6) (2012), pp. 1237-1262 View in ScopusGoogle Scholar [13] B. Gidas, W.M. Ni, L. Nirenberg Symmetry of positive solutions of nonlinear elliptic equations in Rn Ma...
Gou, T., Sun, H.: Solutions of nonlinear Schrodinger equation with fractional Laplacian without the Ambrosetti-Rabinowitz condition. Appl. Math. Comput. 257, 409-416 (2015)T. Gou, H. Sun, Solutions of nonlinear Schr¨odinger equation with fractional Laplacian without the Ambrosetti-Rabinowitz ...
Existence of solutions for the (p, q)-Laplacian equation with nonlocal Choquard reaction. Appl. Math. Lett. 135, 108418 (2023). Article MATH MathSciNet Google Scholar Khater, M. M. In solid physics equations, accurate and novel soliton wave structures for heating a single crystal of ...
Peral Alonso, “Sobolev versus Hölder local minimizer and global multiplicity for some quasilinear elliptic equations,” Commun. Contemp. Math., vol. 2, no. 3, pp. 385–404, 2000) to fractional p-Laplacian. Owing to the nonlinear and nonlocal properties of (−Δ)ps${\left(-{\Delta...
doi:10.1007/s00028-020-00596-9Stanislavova, MilenaStefanov, AtanasSpringer International PublishingJournal of Evolution Equations
We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result relies on variational structure of the problem. To show ...
Marino, L. Modica, S. Spagnolo (Eds.), Partial Differential Equations and the Calculus of Variations, Vol. 1, Birkhäuser, Basel (1989), pp. 401-449 Google Scholar [26] A. Floer, A. Weinstein Nonspreading wave pachets for the packets for the cubic Schrödinger with a bounded ...
(This article belongs to the Special Issue Differential Equations in Applied Mathematics) Download keyboard_arrow_down Download PDF Download PDF with Cover Download XML Download Epub Browse Figures Versions Notes Abstract Based on the second derivative, this paper directly establishes the coin...