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
Kirchhoff‐type critical fractional Laplacian system with convolution and magnetic field
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DOI: 10.1002/mana.202200172
Abstract: In this paper, we consider a class of upper critical Kirchhoff‐type fractional Laplacian system with Choquard nonlinearities and magnetic fields. With the help of the limit index theory and the concentration–compactness principles for fractional Sobolev… read more here.
Keywords: system; type critical; kirchhoff type; laplacian system ... See more keywords
Ground State Solutions for the Choquard Equation With the Lower Critical Exponent and Riesz Fractional Laplacian
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DOI: 10.1002/mma.10894
Abstract: In this study, we explore both the nonexistence and existence of a nonzero solution for the following Choquard equation (CE): −∆u+𝒱(ϰ)u=−∆D0−α2*|u|αN+1|u|αN−1u,inℝN,u∈H1ℝN, where α∈(0,N),N≥3,$$ \alpha \in \left(0,N\right),N\ge 3, $$ * represents the convolution within ℝN$$ {\mathbb{R}}^N… read more here.
Keywords: equation; riesz fractional; ground state; exponent ... 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