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.X. Cabre´ and Y. Sire, Nonlinear equations for fractional Laplacians II: existence, uniqueness, and ...
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 ...
For the fractional Laplacian, some different discrete schemes for fractional derivative operators were proposed [40], [41], [42], [43], but the theoretical analysis is not available when applied to discretize the partial differential equations. Here a simple-and-easy implementation fractional ...
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 ...
Our existence results are based on compact embedding properties for weighted spaces.doi:10.1007/s10884-016-9521-ySecchi, SimoneUniv Milano BicoccaSpringer USJournal of dynamics and differential equationsS. Secchi, On some nonlinear fractional equations involving the Bessel potential, arXiv:1506.03982....
Z Hu,L Wang,P Zhao - 《Electronic Journal of Differential Equations》 被引量: 1发表: 2016年 A priori bounds and multiplicity results for slightly superlinear and sublinear elliptic p-Laplacian equations We consider the following problem p u = h ( x, u ) in , u 鈭 W 1 ,p 0 () , ...
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...
Luo and Zhang [12] proved some existence and nonexistence results about the normalized solutions to the following fractional nonlinear Schrödinger equations with combined nonlinearities: MathML (1.3) After this, Zhen and Zhang [13] obtained the existence and nonexistence results of system (1.3)...
In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden–Fowler-type and half-linear equations. The inequalities obtained here can be used as ...
in elliptic and parabolic equations; especially to pose boundary-value problems. To our nonlocal setting we bring a judicious way of measuring the smoothness of functions for a given set. Let \(D\subset {{{\mathbb {R}}}^d}\) be open. For the sake of gradual introduction we first ...