Nontrivial solutions for the fractional Schrödinger‐Poisson system with subcritical or critical nonlinearities
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DOI: 10.1002/mma.6019
Abstract: In this paper, we are concerned with a class of fractional Schrödinger‐Poisson system involving subcritical or critical nonlinearities. By using the Nehari manifold and variational methods, we obtain the existence and multiplicity of nontrivial solutions. read more here.
Keywords: dinger poisson; fractional schr; critical nonlinearities; poisson system ... See more keywords
On the Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with General Potentials and Super-quadratic Nonlinearity
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DOI: 10.1007/s00009-018-1179-8
Abstract: In this article, we are concerned with the following fractional Schrödinger–Poisson system: $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u+V(x)u+\phi u=f(u)&{} \quad \hbox {in}~\mathbb {R}^{3},\\ (-\Delta )^{t}\phi =u^2&{} \quad \hbox {in}~\mathbb {R}^{3},\\ \end{array} \right. \end{aligned}$$(-Δ)su+V(x)u+ϕu=f(u)inR3,(-Δ)tϕ=u2inR3,where $$03$$2s+2t>3, and $$f\in… read more here.
Keywords: dinger poisson; fractional schr; state solutions; ground state ... See more keywords
A numerical method for solving the time fractional Schrödinger equation
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DOI: 10.1007/s10444-017-9579-z
Abstract: In this article, we proposed a new numerical method to obtain the approximation solution for the time-fractional Schrödinger equation based on reproducing kernel theory and collocation method. In order to overcome the weak singularity of… read more here.
Keywords: numerical method; fractional schr; time fractional; method ... See more keywords
Solutions of the Radial Component of the Fractional Schrödinger Equation Using N-Fractional Calculus Operator
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DOI: 10.1007/s12591-016-0308-8
Abstract: Fractional calculus tecniques are used for the solutions of some classes of differential equations and fractional differential equations. One of the these tecniques is N-fractional calculus operator $$N^{\eta }$$ N η method. We can obtain… read more here.
Keywords: component fractional; fractional calculus; calculus; radial component ... See more keywords
On fractional Schrödinger systems of Choquard type
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DOI: 10.1016/j.jde.2017.04.034
Abstract: Abstract In this article, we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schrodinger–Choquard equation i ∂ t Ψ + ( − Δ ) α… read more here.
Keywords: choquard type; systems choquard; fractional schr; schr dinger ... See more keywords
Fractional Schrödinger Equation with Singular Potentials of Higher Order
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DOI: 10.1016/s0034-4877(21)00016-1
Abstract: In this paper the space-fractional Schrodinger equations with singular potentials are studied. Delta like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of ‘weakened’ solutions, calling them very… read more here.
Keywords: schr dinger; dinger equation; higher order; singular potentials ... See more keywords
FRACTIONAL SCHRÖDINGER–POISSON SYSTEM WITH SINGULARITY: EXISTENCE, UNIQUENESS, AND ASYMPTOTIC BEHAVIOR
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DOI: 10.1017/s0017089520000099
Abstract: Abstract In this paper, we consider the following fractional Schrödinger–Poisson system with singularity \begin{equation*} \left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. \end{equation*} where… read more here.
Keywords: schr dinger; dinger poisson; poisson system; system singularity ... See more keywords
Ground states for fractional Schrödinger equations with critical growth
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DOI: 10.1063/1.5008662
Abstract: In this paper, we study the following critical fractional Schrodinger equation: (−Δ)su+V(x)u=|u|2s*−2u+λf(x,u), x∈RN, where λ > 0, 0 2s, 2s*=2NN−2s, (−Δ)s denotes the fractional Laplacian of order s, and f is a continuous superlinear but subcritical… read more here.
Keywords: ground; fractional schr; states fractional; ground states ... See more keywords
Dissipative character of asymptotics for the nonlinear fractional Schrödinger equation
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DOI: 10.1063/1.5127942
Abstract: We consider the Cauchy problem for the fractional nonlinear Schrodinger equation i∂tu+25∂x52u=λu52u, where λ∈R. We obtain the large time asymptotic behavior of solutions, which has a self-similar behavior and a logarithmic modification compared with the… read more here.
Keywords: dissipative character; character asymptotics; fractional schr; nonlinear fractional ... See more keywords
Infinitely many solutions of fractional Schrödinger–Maxwell equations
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DOI: 10.1063/5.0028800
Abstract: In this article, we investigate the existence of infinitely many solutions to the 3D fractional Schrodinger–Maxwell equations (−Δ)su + V(x)u + ϕu = λf(x, u), (−Δ)sϕ = u2, where 0 < s < 1, λ… read more here.
Keywords: fractional schr; solutions fractional; many solutions; infinitely many ... See more keywords
Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations
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DOI: 10.1080/00207160.2020.1822994
Abstract: This paper develops and analyses a finite difference/spectral-Galerkin scheme for the nonlinear fractional Schrödinger equations with Riesz space- and Caputo time-fractional derivatives. The finite difference approximation is used for the discretization of the Caputo fractional… read more here.
Keywords: dinger equations; space; fractional schr; time ... See more keywords