LAUSR

On the bifurcation results for fractional Laplace equations

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1 Published in 2017 at "Mathematische Nachrichten"

DOI: 10.1002/mana.201600250

Abstract: In this paper, we consider the bifurcation problem for the fractional Laplace equation (−Δ)su=λu+f(λ,x,u)inΩ,u=0inRn∖Ω, where Ω⊂Rn,n>2s(0 read more here.

Keywords: bifurcation results; fractional laplace; results fractional; laplace equations ... See more keywords

Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense

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1 Published in 2019 at "Advances in Applied Clifford Algebras"

DOI: 10.1007/s00006-019-1029-1

Abstract: In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation… read more here.

Keywords: laplace; natural powers; fractional laplace; dirac operators ... See more keywords

Non-negative solutions to fractional Laplace equations with isolated singularity

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0 Published in 2020 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2020.107329

Abstract: Abstract In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish Bocher type theorems on a punctured ball via distributional approach. Then, we develop a few interesting maximum principles… read more here.

Keywords: solutions fractional; fractional laplace; negative solutions; laplace equations ... See more keywords

Spectrum and constant sign solutions for a fractional Laplace problem with sign-changing weight

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1 Published in 2020 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2019.123528

Abstract: Abstract In this paper, we study the spectrum of the fractional Laplace operator with sign-changing weight and show that there exist two simple, isolated principal eigenvalues λ 1 + and λ 1 − . By… read more here.

Keywords: constant sign; fractional laplace; sign solutions; sign ... See more keywords

On some singular problems involving the fractional p(x,.) -Laplace operator

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2 Published in 2021 at "Applicable Analysis"

DOI: 10.1080/00036811.2021.1950693

Abstract: The purpose of the present paper is to study the existence of solutions for the following nonhomogeneous singular problem involving the fractional p(x,.)-Laplace operator {(−Δ)p(x,.)su+|u|q(x)−2u=g... read more here.

Keywords: laplace operator; involving fractional; fractional laplace; singular problems ... See more keywords

Maximum Principle for the Space-Time Fractional Conformable Differential System Involving the Fractional Laplace Operator

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0 Published in 2020 at "Journal of Mathematics"

DOI: 10.1155/2020/7213146

Abstract: In this paper, the authors consider a IBVP for the time-space fractional PDE with the fractional conformable derivative and the fractional Laplace operator. A fractional conformable extremum principle is presented and proved. Based on the… read more here.

Keywords: system; laplace; maximum principle; fractional laplace ... See more keywords

Existence of multiple positive solutions for fractional Laplace problems with critical growth and sign-changing weight in non-contractible domains

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0 Published in 2019 at "Boundary Value Problems"

DOI: 10.1186/s13661-019-1193-1

Abstract: We prove the existence of multiple positive solutions for a fractional Laplace problem with critical growth and sign-changing weight in non-contractible domains. read more here.

Keywords: solutions fractional; fractional laplace; positive solutions; critical growth ... See more keywords