[PDF] Top 20 Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian
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Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian
... In this paper, following the ideas of [12], among others, we consider the properties of the solutions to system (1.1) for different domains . More precisely, we get the following four theorems. Firstly, we consider ... See full document
16
Infinitely many solutions for hemivariational inequalities involving the fractional Laplacian
... many solutions for elliptic boundary value prob- lems without the symmetric functionals is an important topic in nonlinear analysis, hence there are a lot of papers focused on the existence of infinitely ... See full document
23
Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian
... sign-changing solutions of nonlinear elliptic equations have been obtained by combing minimax method with invariant sets of descending flow (see [, ...the nonlinear equation involving the ... See full document
23
Existence of positive solutions to elliptic problems involving the fractional Laplacian
... positive solutions of ...the nonlinear term f (u) is superlinear with respect to u at infinity instead of the asymptot- ically linear condition or Ambrosetti-Rabinowitz condition, which is completely ... See full document
12
Multiple positive solutions for nonlinear coupled fractional Laplacian system with critical exponent
... The fractional Laplacian operator and fractional Sobolev space arise in a quite natural way in many different contexts, such as the thin obstacle problem, finance, phase transitions, anomalous ... See full document
25
A note on the existence and multiplicity of solutions for sublinear fractional problems
... the fractional Sobolev spaces and some preliminary ...multiplicity solutions for fractional Laplacian problems to the one for fractional p-Laplacian ... See full document
15
Existence of ground state solutions to a class of fractional Schrödinger system with linear and nonlinear couplings
... and nonlinear coupling terms both exist, to the best of our knowledge, there has been almost no research on this ...the fractional Laplacian system, we refer the reader to [6–23] and the references ... See full document
16
Positive solution for q fractional four point boundary value problems with p Laplacian operator
... of solutions or positive solutions for boundary value problems involving nonlinear fractional q-difference equations by the use of some well-known fixed point theorems and the upper and ... See full document
14
Analytic and numerical solutions for systems of fractional Schrödinger equation
... finding solutions of the time-fractional nonlinear Schrödinger equation in one and two dimensions, have appeared in quantum ...the fractional Schrödinger type equation of spatial ... See full document
11
Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms
... the fractional Schrödinger–Poisson sys- tems are not so rich as the Schrödinger–Poisson systems ...the fractional Schrödinger–Poisson system with a general nonlinearity in the ... See full document
10
Monotone iterative method for a p-Laplacian boundary value problem with fractional conformable derivatives
... monotone solutions for initial and boundary value ...to nonlinear fractional differential equations, see [15, 33– ...new fractional derivative, which is known as fractional conformable ... See full document
12
Existence and nonexistence of positive solutions for the fractional coupled system involving generalized p Laplacian
... of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different ...positive solutions for the fractional system ... See full document
19
Extremal solutions for p Laplacian fractional differential systems involving the Riemann Liouville integral boundary conditions
... of fractional differential equations involving p- Laplacian operators and nonlocal boundary conditions based on the Riemann-Liouville ...lower solutions and the monotone iteration ... See full document
11
Existence of Solutions for a Class of Elliptic Systems in Involving the Laplacian
... Zhang, “Existence of positive solutions for elliptic systems with nonstandard px-growth conditions via sub-supersolution method,” Nonlinear Analysis: Theory, Methods & Applications, vol.[r] ... See full document
16
Positive bound state solutions for the nonlinear Schrödinger–Poisson systems with potentials
... The fractional Schrödinger equation in (1.2) is an important model in the study of frac- tional quantum mechanics. In Refs. [12, 13], Laskin introduced this equation by expanding the Feynman path integral ... See full document
19
Multiple solutions of a p Laplacian model involving a fractional derivative
... positive solutions to boundary value problems for a fractional differential equation involv- ing a p-Laplacian operator ...standard nonlinear fractional differential ...positive ... See full document
12
Maximum and minimum solutions for a nonlocal p-Laplacian fractional differential system from eco-economical processes
... positive solutions for nonlinear fractional equation with p-Laplacian operator have been reported [–, ...of solutions for the anti-periodic fractional order ... See full document
15
Existence of homoclinic solutions for a class of difference systems involving p Laplacian
... Hamiltonian systems is a classical problem and its importance in the study of the behavior of dynamical systems has been firstly recognized by Poincaré ... See full document
17
Positive solutions of fractional p Laplacian equations with integral boundary value and two parameters
... tional derivative of order δ. By using an upper and lower solution method, the fixed point index theorem and the Schauder fixed point theorem, sufficient conditions are obtained for the problem to have at least one positive ... See full document
15
Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p Laplacian Operator
... of fractional calculus itself as well as its applications, fractional differential equations have been constantly attracting attention of many scholars; see, for example, ... See full document
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