Electronic Journal of Differential Equations
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The Electronic Journal of Differential Equations is hosted by the Department of Mathematics at Texas State University. Since its foundation in 1993, this ejournal has been dedicated to the rapid dissemination of high quality research in mathematics.
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Numerical Solution of a Parabolic Equation with a Weakly Singular Positivetype Memory Term
(Texas State University, Department of Mathematics, 19970604)We find a numerical solution of an initial and boundary value problem. This problem is a parabolic integrodifferential equation whose integral is the convolution product of a positivedefinite weakly singular kernel with ... 
Semilinear Hyperbolic Systems in one Space Dimension with Strongly Singular Initial Data
(Texas State University, Department of Mathematics, 19970828)In this article interactions of singularities in semilinear hyperbolic partial differential equations in R^2 are studied. Consider a simple nonlinear system of three equations with derivatives of Dirac delta functions as ... 
Partial Regularity for Flows of HSurfaces
(Texas State University, Department of Mathematics, 19971120)This article studies regularity of weak solutions to the heat equation for Hsurfaces. Under the assumption that the function H is Lipschitz and depends only on the first two components, the solution has regularity on its ... 
Stable Multiplelayer Stationary Solutions of a Semilinear Parabolic Equation in Twodimensional Domains
(Texas State University, Department of Mathematics, 19971201)We use Γconvergence to prove existence of stable multiplelayer stationary solutions (stable patterns) to a reactiondiffusion equation. Given nested simple closed curves in R2, we give sufficient conditions on their ... 
A Spectral Problem with an Indefinite Weight for an Elliptic System
(Texas State University, Department of Mathematics, 19971129)We establish the completeness and the summability in the sense of AbelLidskij of the root vectors of a nonselfadjoint elliptic problem with an indefinite weight matrix and the angular distribution of its eigenvalues. 
Solutions to Perturbed Eigenvalue Problems of the pLaplacian in R(N)
(Texas State University, Department of Mathematics, 19970715)Using a variational approach, we investigate the existence of solutions for nonautonomous perturbations of the pLaplacian eigenvalue problem Δpu=f(x,u) in R(N). Under the assumptions that the primitive F(x,u) of ... 
Analysis of the Mushy Region in Conductionconvection Problems with Change of Phase
(Texas State University, Department of Mathematics, 19970130)A conductionconvection problem with change of phase is studied, where convective motion of the liquid affects the change of phase. The mushy region is the portion of the system to which temperature and enthalpy do not ... 
Stable Evaluation of Differential Operators and Linear and Nonlinear Multiscale Filtering
(Texas State University, Department of Mathematics, 19970910)Diffusion processes create multiscale analyses, which enable the generation of simplified pictures, where for increasing scale the image gets sketchier. In many practical applications the ``scaled image'' can be characterized ... 
Numerical Calculation of Singularities for GinzburgLandau Functionals
(Texas State University, Department of Mathematics, 19970618)We give results of numerical calculations of asymptotic behavior of critical points of a GinzburgLandau functional. We use both continuous and discrete steepest descent in connection with Sobolev gradients in order to ... 
A Note on Very Weak PHarmonic Mappings
(Texas State University, Department of Mathematics, 19971219)We prove a new a priori estimate for very weak pharmonic mappings when p is close to two. This sheds some light on a conjecture posed by Iwaniec and Sbordone. 
On Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations
(Texas State University, Department of Mathematics, 19970130)We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem { −div (∇up−2∇u) = λa(x)up−2u + b(x)uγ−2u, x ∈ Ω, ∂u = 0, x ∈ ∂Ω , ∂n where Ω is a smooth ... 
Positive Solutions and Nonlinear Multipoint Conjugate Eigenvalue Problems
(Texas State University, Department of Mathematics, 19971219)Values of λ are determined for which there exist solutions in a cone of the nth order nonlinear differential equation, u(n) = λa(t)f(u), 0 <t< 1, satisfying the multipoint boundary conditions, u(j)(ai) = 0, 0 ≤ j ≤ ni−1, ... 
On a Mixed Problem for a Coupled Nonlinear System
(Texas State University, Department of Mathematics, 19970306)In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system utt − M ( ∇u2dx)∆u + uρu + θ = f Ω θt − ∆θ + ut = g where M is a positive real function, ... 
Stability of a Linear Oscillator with Variable Parameters
(Texas State University, Department of Mathematics, 19971029)A criterion of asymptotic stability for a linear oscillator with variable parameters is obtained. It is shown that this criterion is close to a necessary and sufficient conditions of asymptotic stability. An instability ... 
Initial Value Problems for Nonlinear Nonresonant Delay Differential Equations with Possibly Infinite Delay
(Texas State University, Department of Mathematics, 19971219)We study initial value problems for scalar, nonlinear, delay dif ferential equations with distributed, possibly infinite, delays. We consider the initial value problem { x(t) = ϕ(t), t ≤ 0 x' (t)+ g(t, s, x(t), x(t − ... 
Existence and Multiplicity Results for Homoclinic Orbits of Hamiltonian Systems
(Texas State University, Department of Mathematics, 19970326)Homoclinic orbits play an important role in the study of qualitative behavior of dynamical systems. Such kinds of orbits have been studied since the time of Poincare. In this paper, we discuss how to use variational methods ... 
Hill's Equation for a Homogeneous Tree
(Texas State University, Department of Mathematics, 19971218)The analysis of Hill’s operator −D2 + q(x) for q even and periodic is extended from the real line to homogeneous trees T. Generalizing the classical problem, a detailed analysis of Hill’s equation and its related operator ... 
A Multiplicity Result for a Class of Quasilinear Elliptic and Parabolic Problems
(Texas State University, Department of Mathematics, 19970422)We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichletperiodic boundary conditions. We assume that the primitive ... 
Behaviour Near the Boundary for Solutions of Elasticity Systems
(Texas State University, Department of Mathematics, 19970731)In this article we study the behaviour near the boundary for weak solutions of the system ull − µ∆u − (λ + µ)∇(α(x) div u) = h, with u(x, t) = 0 on the boundary of a domain Ω ∈ Rn, and u(x, 0) = u0, ul(x, 0) = u1 in ... 
Complex Dynamical Systems on Bounded Symmetric Domains
(Texas State University, Department of Mathematics, 19971029)We characterize those holomorphic mappings which are the infinitesimal generators of semiflows on bounded symmetric domains in complex Banach spaces.