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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On a Mixed Problem for a Linear Coupled System with Variable Coefficients
(Texas State University, Department of Mathematics, 19980213)We prove existence, uniqueness and exponential decay of solutions to the mixed problem u" (x,t)  μ(t)Δu(x,t) + Σn i=1 ∂θ/∂xi (x,t) = 0, θ' (x,t)  Δθ(x,t) + Σn i=1 ∂u'/∂xi (x,t) = 0, with a suitable boundary damping, ... 
Eigenvalue Comparisons for Differential Equations on a Measure Chain
(Texas State University, Department of Mathematics, 19981219)The theory of u0positive operators with respect to a cone in a Banach space is applied to eigenvalue problems associated with the second order Δdifferential equation (often referred to as a differential equation on a ... 
Decay of Solutions of a Degenerate Hyperbolic Equation
(Texas State University, Department of Mathematics, 19980828)This article studies the asymptotic behavior of solutions to the damped, nonlinear wave equation ü + yů  m(∇u2)∆u = ƒ(x,t), for x ∈ Ω, t ≥ 0 u(x,0) = g(x), ů(x,0) = h(x), for x ∈ Ω u(x,t) = 0, for x ∈ ∂Ω t ≥ ... 
Some Remarks on a Second Order Evolution Equation
(Texas State University, Department of Mathematics, 19980702)We prove the strong asymptotic stability of solutions to a second order evolution equation when the LaSalle's invariance principle cannot be applied due to the lack of monotonicity and compactness. 
Global Attractor and Finite Dimensionality for a Class of Dissipative Equations of BBM's Type
(Texas State University, Department of Mathematics, 19981013)In this work we study the Cauchy problem for a class of nonlinear dissipative equations of BenjaminBonaMahony's type. We discuss the existence of a global attractor and estimate its Hausdorff and fractal dimensions. 
Exponential Stability of a Von Karman Model with Thermal Effects
(Texas State University, Department of Mathematics, 19980227)A onedimensional Von Karman model with thermal effects is studied. We derive the equations that constitute the mathematical model, and prove existence and uniqueness of a global solution. Then using Lyapunov functions, ... 
Adjoint and Selfadjoint Differential Operators on Graphs
(Texas State University, Department of Mathematics, 19980226)A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as ... 
Barriers on Cones for Degenerate Quasilinear Elliptic Operators
(Texas State University, Department of Mathematics, 19980417)Barrier functions w = xλΦ(ω) are constructed for the first boundary value problem as well as for the mixed boundary value problem for quasilinear elliptic second order equation of divergent form with triple degeneracy ... 
On Forced Periodic Solutions of Superlinear Quasiparabolic Problems
(Texas State University, Department of Mathematics, 19980530)We study the existence of periodic solutions for a class of quasiparabolic equations involving the pLaplacian (or any other nonlinear operators of similar class) perturbed by nonlinear terms and forced by rather irregular ... 
A Minmax Principle, Index of the Critical Point, and Existence of Signchanging Solutions to Elliptic Boundary Value Problems
(Texas State University, Department of Mathematics, 19980130)In this article we apply the minmax principle we developed in [6] to obtain signchanging solutions for superlinear and asymptotically linear Dirichlet problems. We prove that, when isolated, the local degree of any solution ... 
Existence and Boundary Stabilization of a Nonlinear Hyperbolic Equation with Timedependent Coefficients
(Texas State University, Department of Mathematics, 19980310)In this article, we study the hyperbolic problem K(x,t)u{tt}  \∑n j=1 (a(x,t)uxj) + F(x,t,u,∇u) = 0 u = 0 on Γ1, ∂u/∂v + ß(x)ut = 0 on Γ0 u(0) = u0, ut(0) = u1 in Ω, where Ω is a bounded region in Rn whose ... 
Existence of Axisymmetric Weak Solutions of the 3D Euler Equations for NearVortexSheet Initial Data
(Texas State University, Department of Mathematics, 19981015)We study the initial value problem for the 3D Euler equation when the fluid is inviscid and incompressible, and flows with axisymmetry and without swirl. On the initial vorticity ω0, we assumed that ω0/r belongs to L(log ... 
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 ... 
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 ... 
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 ... 
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. 
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 ... 
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 ... 
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.