fractional laplacian
Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian
... the fractional Laplacian is nonlocal, that is, it does not act by pointwise differenti- ation but as a global integral with respect to a singular kernel, this is the main difficulty in studying problems ...
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Infinitely many solutions for hemivariational inequalities involving the fractional Laplacian
... local Laplacian and the p-Laplacian, see for exam- ple [11, ...involving fractional Laplacian has received attention of some authors via variational methods ...nonlocal fractional ...
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Existence of positive solutions to elliptic problems involving the fractional Laplacian
... Chang, XJ: Ground state solutions of asymptotically linear fractional Schrödinger equations.. Chang, XJ, Wang, ZQ: Ground state of scalar field equations involving a fractional Laplacian [r] ...
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Infinitely many solutions for fractional Laplacian problems with local growth conditions
... where < s < < p < + ∞ , N > s, ⊂ R N is an open bounded domain with smooth boundary, f (x, t) is a Carathéodory function defined on × (–δ, δ) for some δ > , and (–) s is known as the ...
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Topological arguments for an elliptic equation involving the fractional Laplacian
... Recently, several studies have been performed for classical elliptic equations similar to () and () but with the fractional conformal Laplacians instead of the Laplacian. This op- erator is introduced ...
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Fractional diffusion: biological models and nonlinear problems driven by the s-power of the Laplacian.
... Recently in the mathematic field the study of the fractional spaces and opera- tors became very important. Infact, many biological phenomenas are strictly connect with the nonlocal diffusion, certainly more ...
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On some properties of a class of fractional stochastic heat equations
... The Dirichlet heat kernel for the operator L := −(−) α/ 2 −(−) α/ ¯ 2 has been studied in [3]. Since α ¯ ≤ α, it is known that for small times, the behaviour of the heat kernel estimates is dominated by the ...
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A note on the existence and multiplicity of solutions for sublinear fractional problems
... the fractional Sobolev spaces and some preliminary ...for fractional Laplacian problems to the one for fractional p-Laplacian ...
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Non-existence of Global Solutions to a Wave Equation with Fractional Damping
... of fractional diffusion- Wave equation via lossy media obeying frequency power ...Holm: Fractional Laplacian, Levy stable distribution and time-space models for linear and nonlinear frequency ...
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Eigenfunctions and Fundamental Solutions of the Fractional Two Parameter Laplacian
... Theorem 2.6. In case (ii) functions 2.26 and 2.30 represent eigenfunctions of the fractional Laplacian 2.4 and expressions 2.28 and 2.31 are unique classical fundamental solutions subject to conditions ...
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Existence results for a coupled system of fractional differential equations with p-Laplacian operator and infinite-point boundary conditions
... of fractional p- Laplacian differential equations is mainly at two-point boundary value ...for fractional p-Laplacian differential equations with multi-point and even infinite- point at resonance ...
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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, ...
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Existence of Positive Solutions for a Coupled System of (p, q)-Laplacian Fractional Higher Order Boundary Value Problems
... q)-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach ...
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Existence of solutions of fractional boundary value problems with p-Laplacian operator
... In [], Liu et al. studied the solvability of the Caputo fractional differential equation with boundary value conditions involving the p-Laplacian operator. The existence and uniqueness of the problem is ...
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Positive solutions of fractional p Laplacian equations with integral boundary value and two parameters
... where D η–2 0+ , D k–2 0+ are the standard Riemann–Liouville fractional derivative, n – 1 < η ≤ n, η ≥ 4, 2 ≤ k ≤ n – 2, α, β, γ , δ > 0. 0 1 u(s) dA(s) and 0 1 u(s) dB(s) denote the Riemann– Stieltjes ...
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Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems
... For the uniqueness of solution for fractional differential equation (2.24), we apply theorem (2.6). In equation (2.24), we have α = β = 2.5, ξ = γ = 1/2, a(t) = t, f (u(t)) = √ u(t) it is clear that (2.24) satisfy ...
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Existence of Solutions for Boundary Value Problems of Vibration Equation with Fractional Derivative
... In this paper, we investigate the solvability of boundary value problems for a class of vibration differential equation describing the fractional order damped system with signal stimulus. By presenting kernel ...
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Existence of solutions for discrete fractional boundary value problems with a p Laplacian operator
... The remainder of this paper is organized as follows. Section preliminarily provides some necessary background material for the theory of discrete fractional calculus. In Sec- tion , the main existence result ...
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Existence and uniqueness results for q fractional difference equations with p Laplacian operators
... Motivated by the previously mentioned works, we will consider the existence of solu- tions of q-fractional p-Laplacian BVP with two-point boundary conditions. The main dif- ficulty is that, for p = , it is ...
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The uniqueness of solution for a fractional order nonlinear eigenvalue problem with p Laplacian operator
... where < β ≤ , < α ≤ , ≤ a ≤ , < ξ < . By using Krasnosel’skii’s fixed point the- orem and the Leggett-Williams theorem, some sufficient conditions for the existence of positive solutions to the above ...
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