This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves ψ = u(x)e in equilibrium with a purely electrostatic field E = −∇φ(x). We assume an homogeneous Dirichlet boundary condition on u and an inhomogeneous Neumann boundary condition on φ. In the “linear” case we characterize the existence of nontrivial solutions for s...

In this paper, we consider a semilinear parabolic equation ut = ∆u + u q ∫ t 0 u(x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u|∂Ω×(0,+∞) = ∫ Ω φ(x, y)u (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.

The main purpose of this paper is to establish the existence of nontrivial solutions to semilinear polyharmonic equations with exponential growth at the subcritical or critical level. This growth condition is motivated by the Adams inequality [1] of Moser-Trudinger type. More precisely, we consider the semilinear elliptic equation (−∆) u = f(x, u), subject to the Dirichlet boundary condition u ...

Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green’s function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. LAGNESE, Boundary Stabilization of Twin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case—where rotational forces are neglected—in [Z. ...

in this paper, nonlinear vibration and instability response of an embedded pipe conveying viscose fluid is investigated. the pipe is considered as a timoshenko beam embedded on an elastic foundation which is simulated by spring constant of the winkler-model and the shear constant of the pasternak-model. the external flow force, acting on the beam in the direction of the flexural displacement is...

We consider the Neumann boundary value problem for harmonic maps in an annular domain with a large number of small holes. On the boundary of the domain the degree condition is prescribed. We obtain an effective (homogenized) anisotropic nonlinear problem. We also discuss applications of these results to homogenized description of superconducting composites and superfluidity.