On a scattering length for additive functionals and spectrum of fractional Laplacian with a non‐local perturbation
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DOI: 10.1002/mana.201800254
Abstract: In this paper we study the scattering length for positive additive functionals of symmetric stable processes on Rd . The additive functionals considered here are not necessarily continuous. We prove that the semi‐classical limit of… read more here.
Keywords: perturbation; scattering length; fractional laplacian; non local ... See more keywords
On a class of p‐fractional Laplacian equations with potential depending on parameter
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DOI: 10.1002/mma.6078
Abstract: We discuss the existence of solutions for a class of nonlinear equations driven by the fractional p‐Laplacian operator of the form (−Δ)psu+λsV(x,λ)|u|p−2u=f(x,u)inRN, where 0ps and λ is a positive parameter. By combining variational techniques with… read more here.
Keywords: class; equations potential; potential depending; class fractional ... See more keywords
The Positive Solutions for Integral Boundary Value Problem of Fractional p-Laplacian Equation with Mixed Derivatives
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DOI: 10.1007/s00009-017-0895-9
Abstract: In this paper, we consider a class of integral boundary value problems of fractional p-Laplacian equation, which involve both Riemann–Liouville fractional derivative and Caputo fractional derivative. By using the generalization of Leggett–Williams fixed point theorem,… read more here.
Keywords: fractional laplacian; positive solutions; value; integral boundary ... See more keywords
Four Solutions for Fractional p-Laplacian Equations with Asymmetric Reactions
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DOI: 10.1007/s00009-021-01860-z
Abstract: We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p -Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at… read more here.
Keywords: asymmetric reactions; solutions fractional; fractional laplacian; laplacian equations ... See more keywords
Nonnegative solutions for the fractional Laplacian involving a nonlinearity with zeros
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DOI: 10.1007/s00229-021-01275-w
Abstract: We study the nonlocal nonlinear problem $$\begin{aligned} \left\{ \begin{array}[c]{lll} (-\Delta )^s u = \lambda f(u) &{} \text{ in } \Omega , \\ u=0&{}\text{ on } \mathbb {R}^N{\setminus }\Omega , \quad (P_{\lambda }) \end{array} \right. \end{aligned}$$… read more here.
Keywords: fractional laplacian; lambda lambda; solutions fractional; lambda ... See more keywords
The spectral collocation method for efficiently solving PDEs with fractional Laplacian
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DOI: 10.1007/s10444-017-9564-6
Abstract: We derive a spectral collocation approximation to the fractional Laplacian operator based on the Riemann-Liouville fractional derivative operators on a bounded domain Ω = [a, b]. Corresponding matrix representations of (−△)α/2 for α ∈ (0,1)… read more here.
Keywords: method efficiently; collocation method; spectral collocation; fractional laplacian ... See more keywords
Periodic solutions of a semilinear elliptic equation with a fractional Laplacian
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DOI: 10.1007/s11784-016-0357-1
Abstract: We consider periodic solutions of the following problem associated with the fractional Laplacian $$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$(-∂xx)su(x)+F′(u(x))=0,u(x)=u(x+T),inR,where $$(-\partial _{xx})^s$$(-∂xx)s denotes the usual fractional Laplace operator with… read more here.
Keywords: equation fractional; solutions semilinear; periodic solutions; fractional laplacian ... See more keywords
Existence of three solutions for perturbed nonlinear fractional p-Laplacian boundary value systems with two control parameters
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DOI: 10.1007/s11868-020-00354-y
Abstract: In this paper, we use two control parameters to study a class of perturbed nonlinear fractional p-Laplacian differential systems, where we prove the existence of three weak solutions by using the variational method and Ricceri’s… read more here.
Keywords: fractional laplacian; two control; perturbed nonlinear; nonlinear fractional ... See more keywords
On the fractional Laplacian of variable order
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DOI: 10.1007/s13540-021-00003-1
Abstract: We present a novel definition of variable-order fractional Laplacian on $${\mathbb {R}}^n$$ R n based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the… read more here.
Keywords: variable order; order fractional; fractional laplacian; laplacian variable ... See more keywords
Multiple Positive Solutions for a Fractional Laplacian System with Critical Nonlinearities
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DOI: 10.1007/s40840-016-0432-1
Abstract: In this paper, we study the following nonlinear fractional Laplacian system with critical exponent $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u=\lambda |u|^{p-2}u+\frac{2\alpha }{\alpha +\beta }|u|^{\alpha -2}u|v|^{\beta }, &{}\quad \hbox {in} \;\ \Omega ,\\ (-\Delta )^{s}v=\mu |v|^{p-2}v+\frac{2\beta }{\alpha… read more here.
Keywords: laplacian system; system critical; fractional laplacian; beta ... See more keywords
Matrix Transfer Technique for Anomalous Diffusion Equation Involving Fractional Laplacian
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DOI: 10.1016/j.apnum.2021.10.006
Abstract: Abstract The fractional Laplacian, ( − △ ) s , s ∈ ( 0 , 1 ) , appears in a wide range of physical systems, including Levy flights, some stochastic interfaces, and theoretical physics… read more here.
Keywords: equation involving; involving fractional; matrix transfer; fractional laplacian ... See more keywords