Sire, Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions, Trans. Amer. Math. Soc. 367 (2015), no. 2, 911-941.Cabre X., Sire Y., Nonlinear equations
Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), pp. 23-53 View PDFView articleCrossrefView in ScopusGoogle Scholar [19] L. Caffarelli, L. Silvestre An extension problems related ...
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 ...
Xia, Liouville type theorems for nonlinear elliptic equations and systems involving fractional laplacian in the half space, Calc. Var. Partial Differential Equations, DOI 10.1007/s00526-014-0727-8.A. Quaas and A. Xia: Liouville type theorems for nonlinear elliptic equations and systems involving ...
Jiang, M, Zhong, S: Existence of solutions for nonlinear fractional q-difference equations with Riemann-Liouville type q-derivatives. J. Appl. Math. Comput. 47, 429-459 (2015)M. Jiang, S. Zhong, Existence of solutions for nonlinear fractional q-difference equations with riemann-liouville type...
Xiang, MQ, Zhang, BL, Radulescu, V: Existence of solutions for perturbed fractional p-Laplacian equations. J. Differ. Equ. 260, 1392-1413 (2016) Article MathSciNet MATH Google Scholar Di Nezza, E, Palatucci, G, Valdinoci, E: Hitchhiker’s guide to the fractional Sobolev spaces. Bul...
We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization...
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 ...
By using Mathematica to solve these equations, we can get the values of the unknowns pi,qi, m, and c, which will be utilized to obtain the answer to Eq. (3). The extended simple equation method We suppose the trial solution of the partial differential equation (PDE) of Eq. (1) ...
utilized a fast compact difference method and further analyzed the pointwise error estimate for the complex Ginzburg-Landau equations in two dimension [24,25]. Show abstract Well-posedness of space fractional Ginzburg–Landau equations involving the fractional Laplacian arising in a Bose–Einstein ...