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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue

Vol 12 - Issue 4 (September 2021)

Advances in Pure and Applied Mathematics


List of Articles

Multiplicity of solutions for a nonhomogeneous problem involving a potential in Orlicz-Sobolev spaces
NAWAL IRZI

This paper is devoted to the study of the nonhomogeneous problem
div(a(|u|)u)+a(|u|)u=λV(x)|u|m(x)2uμg(x,u) in Ω, u=0 on Ω, where Ω is a bounded smooth domain in RN,λ,μ are positive real numbers, V(x) is a potential, m:¯Ω(1,) is a continuous function, a is mapping such that φ(|t|)t is increasing homeomorphism from ℝ to ℝ and g:¯Ω× is a continuous function. We establish there main results with various assumptions, the first one asserts that any λ0> is an eigenvalue of our problem. The second Theorem states the existence of a constant λ such that every λ(0,λ) is an eigenvalue of the problem. While the third Theorem claims the existence of a constant λ such that every λ[λ,) is an eigenvalue of the problem. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.


General Decay Of A Nonlinear Viscoelastic Wave: Equation With Boundary Dissipation
Amel Boudiaf, Salah Drabla

In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satisfies g(t)ξ(t)gp(t),t0,1p32. This work generalizes and improves earlier results in the literature.


Scattering theory in weighted L2 space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
VAN DUONG DINH

In this paper, we consider the following inhomogeneous nonlinear Schrödinger equation (INLS)
itu+Δu+μ |x|b|u|αu=0,(t,x)×d
with b,α > 0. First, we revisit the local well-posedness in H1(d) for (INLS) of Guzmán [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] and give an improvement of this result in the two and three spatial dimensional cases. Second, we study the decay of global solutions for the defocusing (INLS), i.e. μ=1 when 0 < α < α where α=42bd2 for d3, and α= for d=1,2
by assuming that the initial data belongs to the weighted L2 space Σ={uH1(d): |x|uL2(d)}. Finally, we combine the local theory and the decaying property to show the scattering in Σ for the defocusing (INLS) in the case α < α < α, where α=42bd.


Exponential stability of discrete-time damped Schrödinger equation
Imen Nouira, Moez Khenissi

This article concerns the discrete-time problem of the damped Schrödinger equation in a bounded domain and the internal stabilization problem is considered. We constructed a well-posed discrete-time scheme and we proved the exponential stability. Numerical simulations are presented to illustrate the theoretical results.