Asymptotic Analysis - Volume 88, issue 3

Authors: Cuevas, Claudio | Choquehuanca, Mario | Soto, Herme

Article Type: Research Article

Abstract: Let X be an arbitrary Banach space. This work deals with the asymptotic behavior, the continuity and the compactness properties of solutions of the non-linear Volterra difference equation in X described by u(n+1)=λΣj=−∞ n a(n−j)u(j)+f(n,u(n)), n∈Z, for λ in a distinguished subset of the complex plane, where a(n) is a complex summable sequence and the perturbation f is a non-Lipschitz nonlinearity. Concrete applications to control systems and integro-difference equations are given.

Keywords: Volterra difference equation, perturbation theory, asymptotic behavior, continuity properties, compactness properties

DOI: 10.3233/ASY-131213

Citation: Asymptotic Analysis, vol. 88, no. 3, pp. 125-164, 2014

Authors: Chen, Huyuan | Véron, Laurent

Article Type: Research Article

Abstract: Let Ω⊂RN (N≥2) be a bounded C2 domain containing 0, 0<α<1 and 0<p<N/(N−2α). If δ0 is the Dirac mass at 0 and k>0, we prove that the weakly singular solution uk of (Ek ) (−Δ)α u+up =kδ0 in Ω, which vanishes in Ωc , is a classical solution of (E* ) (−Δ)α u+up =0 in Ω\{0} with the same outer data. Let A=[N/2α,1+2α/N) for N=2,3 and (√5−1)/4N<α<1, otherwise, A=∅; we derive that uk converges to ∞ in whole Ω as k→∞ for p∈(0,1+2α/N)\A, while the limit of uk is a strongly singular solution …of (E* ) for 1+2α/N<p<N/(N−2α). Show more

Keywords: fractional Laplacian, Dirac mass, isolated singularity, weak solution, weakly singular solution, strongly singular solution

DOI: 10.3233/ASY-141216

Citation: Asymptotic Analysis, vol. 88, no. 3, pp. 165-184, 2014

Authors: Capdeboscq, Yves

Article Type: Correction

Abstract: Related article: http://iospress.metapress.com/content/elt156k8607uh516/

DOI: 10.3233/ASY-141240

Citation: Asymptotic Analysis, vol. 88, no. 3, pp. 185-186, 2014