In this paper we study the nonexistence of -nite Morse index solutions of the following Neumann boundary value problems
In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satis-es g’ (t) ≤ – ξ (t) g p (t) , t ≥ t 0, 1 ≤ p ≤ 3 ⁄ 2. This work generalizes and improves earlier results in the literature.
In this article, we study initial value problem for the zero-pressure gas dynamics system in non conservative form and the associated adhesion approximation. We use adhesion approximation and modi-ed adhesion approximation in the construction of weak asymptotic solution. First we prove a general existence result for the adhesion model for the initial velocity component in Hs for s > (n ⁄ 2) + 1 and the initial data for the density component being a C1 function. Using this, we construct weak asymptotic solution for the system with initial velocity in L2 ∩ L∞ and the initial density being a bounded Borel measure. Then we make a detailed analysis of the explicit formula for the weak asymptotic solution and generalized solution for the plane-wave type initial data.
This paper is devoted to the study of the nonhomogeneous problem –div(a(|∇u|)∇u) + a(|u|)u = λV (x)|u|m(x)-2u – μg(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 × ℝ → ℝ is a continuous function. We establish there main results with various assumptions, the first one asserts that any λ > 0 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.
This paper is concerned with the existence of an eigenvalue for a p(x)-biharmonic Kirchhoff problem with Navier boundary condition. Under some suitable conditions, we establish that any λ > 0 is an eigenvalue . The proofs combine variational methods with energy estimates. The main results of this paper improve and generalize the previous one introduced by Kefi and Rădulescu (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 439-463).