Existence and Multiplicity of Solutions for Fractional Elliptic Problems with Discontinuous Nonlinearities
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DOI: 10.1007/s00009-018-1188-7
Abstract: We consider the following fractional elliptic problem: $$\begin{aligned} (P)\left\{ \begin{array}{ll} (-\Delta )^s u = f(u) H(u-\mu )&{} \quad \text{ in } \ \Omega ,\\ u =0 &{}\quad \text{ on } \ \mathbb{{R}}^n {\setminus } \Omega… read more here.
Keywords: multiplicity solutions; existence multiplicity; solutions fractional; fractional elliptic ... See more keywords
Bifurcation results for a fractional elliptic equation with critical exponent in $$\mathbb {R}^n$$Rn
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DOI: 10.1007/s00229-016-0878-3
Abstract: In this paper we study some nonlinear elliptic equations in $${\mathbb R}^n$$Rn obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$\begin{aligned} (-\Delta )^s u = \varepsilon \,h\,u_+^q + u_+^p… read more here.
Keywords: bifurcation results; fractional elliptic; results fractional; elliptic equation ... See more keywords
Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations
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DOI: 10.1016/j.aim.2022.108279
Abstract: We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulæ… read more here.
Keywords: strong unique; elliptic equations; fractional elliptic; local asymptotics ... See more keywords
Nonlinear fractional elliptic systems with boundary measure data: Existence and a priori estimates
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DOI: 10.1016/j.jmaa.2019.03.034
Abstract: Abstract We are concerned with positive solutions of the fractional elliptic system ( E ) { ( − Δ ) s u = f ( v ) in Ω , ( − Δ ) s… read more here.
Keywords: positive solutions; nonlinear fractional; elliptic systems; existence ... See more keywords
Fast and slow decay solutions for supercritical fractional elliptic problems in exterior domains
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DOI: 10.1017/prm.2020.91
Abstract: We consider the fractional elliptic problem: where B1 is the unit ball in ℝ N , N ⩾ 3, s ∈ (0, 1) and p > (N + 2s)/(N − 2s). We prove that this problem has infinitely many solutions with slow decay O(|x|−2s/(p−1)) at… read more here.
Keywords: fast slow; decay solutions; fractional elliptic; slow decay ... See more keywords