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**public sources and our publisher partners.**We investigate stable solutions of elliptic equations of the type where n ≥ 2, s ∈ (0, 1), λ ≥0 and f is any smooth positive superlinear function. The operator (− Δ) s stands for the fractional… Continue Reading

This is the first of two articles dealing with the equation $(-\Delta)^{s} v= f(v)$ in $\mathbb{R}^{n}$, with $s\in (0,1)$, where $(-\Delta)^{s}$ stands for the fractional Laplacian ---the… Continue Reading

This paper, which is the follow-up to part I, concerns the equation (-Delta)(s)v + G'(v) = 0 in R-n, with s is an element of (0, 1), where (-Delta)(s) stands for the fractional Laplacian-the… Continue Reading

We discuss properties (optimal regularity, non-degeneracy, smoothness of the free boundary...) of a variational interface problem involving the fractional Laplacian; Due to the non-locality of the… Continue Reading

We deal with symmetry properties for solutions of nonlocal equations of the type
(−Δ)sv=f(v)in Rn,
where s∈(0,1) and the operator (−Δ)s is the so-called fractional Laplacian. The study of this… Continue Reading

Local Analysis of Solutions of Fractional Semi-Linear Elliptic Equations with Isolated Singularities

In this paper, we study the local behaviors of nonnegative local solutions of fractional order semi-linear equations $${(-\Delta )^\sigma u=u^{\frac{n+2\sigma}{n-2\sigma}}}$$(-Δ)σu=un+2σn-2σ with an… Continue Reading

This paper is devoted to the asymptotic analysis of a fractional version of the Ginzburg–Landau equation in bounded domains, where the Laplacian is replaced by an integro-differential operator… Continue Reading

Let $\sigma\in(0,1)$ with $\sigma\neq\frac{1}{2}$. We investigate the fractional nonlinear Schr\"odinger equation in $\mathbb R^d$: $$i\partial_tu+(-\Delta)^\sigma u+\mu|u|^{p-1}u=0,\, u(0)=u_0\in… Continue Reading

Water science and technology : a journal of the…

Taking account of the high specificity of the organic load of winery effluents, a new biophysical treatment using the stripping of ethanol combined with a final concentration by evaporation has been… Continue Reading

Solutions to nonlocal equations with measurable coefficients are higher differentiable.
Specifically, we consider nonlocal integrodifferential equations with measurable coefficients whose model is… Continue Reading