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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 e-journal has been dedicated to the rapid dissemination of high quality research in mathematics.

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Recent Submissions

  • On a Mixed Problem for a Linear Coupled System with Variable Coefficients 

    Clark, H. R.; San Gil Jutuca, L. P.; Milla Miranda, M. (Texas State University, Department of Mathematics, 1998-02-13)
    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 

    Chyan, Chuan Jen; Davis, John M.; Henderson, Johnny; Yin, William K. C. (Texas State University, Department of Mathematics, 1998-12-19)
    The theory of u0-positive operators with respect to a cone in a Banach space is applied to eigenvalue problems associated with the second order Δ-differential equation (often referred to as a differential equation on a ...
  • Decay of Solutions of a Degenerate Hyperbolic Equation 

    Dix, Julio G. (Texas State University, Department of Mathematics, 1998-08-28)
    This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation ü + yů - m(||∇u||2)∆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 

    Aassila, Mohammed (Texas State University, Department of Mathematics, 1998-07-02)
    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 

    Astaburuaga, M. A.; Bisognin, E.; Bisognin, V.; Fernandez, C. (Texas State University, Department of Mathematics, 1998-10-13)
    In this work we study the Cauchy problem for a class of nonlinear dissipative equations of Benjamin-Bona-Mahony'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 

    Benabdallah, Assia; Teniou, Djamel (Texas State University, Department of Mathematics, 1998-02-27)
    A one-dimensional 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 Self-adjoint Differential Operators on Graphs 

    Carlson, Robert (Texas State University, Department of Mathematics, 1998-02-26)
    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 

    Borsuk, Michail; Portnyagin, Dmitriy (Texas State University, Department of Mathematics, 1998-04-17)
    Barrier functions w = |x|λΦ(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 Quasi-parabolic Problems 

    Boldrini, Jose Luiz; Crema, Janete (Texas State University, Department of Mathematics, 1998-05-30)
    We study the existence of periodic solutions for a class of quasi-parabolic equations involving the p-Laplacian (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 Sign-changing Solutions to Elliptic Boundary Value Problems 

    Castro, Alfonso; Cossio, Jorge; Neuberger, John M. (Texas State University, Department of Mathematics, 1998-01-30)
    In this article we apply the minmax principle we developed in [6] to obtain sign-changing 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 Time-dependent Coefficients 

    Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Soraino, J. A. (Texas State University, Department of Mathematics, 1998-03-10)
    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 3-D Euler Equations for Near-Vortex-Sheet Initial Data 

    Chae, Dongho; Imanuvilov, Oleg Yu (Texas State University, Department of Mathematics, 1998-10-15)
    We study the initial value problem for the 3-D 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 Positive-type Memory Term 

    Slodicka, Marian (Texas State University, Department of Mathematics, 1997-06-04)
    We find a numerical solution of an initial and boundary value problem. This problem is a parabolic integro-differential equation whose integral is the convolution product of a positive-definite weakly singular kernel with ...
  • Partial Regularity for Flows of H-Surfaces 

    Wang, Changyou (Texas State University, Department of Mathematics, 1997-11-20)
    This article studies regularity of weak solutions to the heat equation for H-surfaces. 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 

    Travers, Kirsten E. (Texas State University, Department of Mathematics, 1997-08-28)
    In this article interactions of singularities in semilinear hyperbolic partial differential equations in R^2 are studied. Consider a simple non-linear system of three equations with derivatives of Dirac delta functions as ...
  • A Note on Very Weak P-Harmonic Mappings 

    Kinnunen, Juha; Zhou, Shulin (Texas State University, Department of Mathematics, 1997-12-19)
    We prove a new a priori estimate for very weak p-harmonic 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 Conduction-convection Problems with Change of Phase 

    O'Leary, Mike (Texas State University, Department of Mathematics, 1997-01-30)
    A conduction-convection 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 p-Laplacian in R(N) 

    Marcos, Joao B. do O (Texas State University, Department of Mathematics, 1997-07-15)
    Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem Δpu=f(x,u) in R(N). Under the assumptions that the primitive F(x,u) of ...
  • Stable Multiple-layer Stationary Solutions of a Semilinear Parabolic Equation in Two-dimensional Domains 

    Nascimento, Arnaldo Simal do (Texas State University, Department of Mathematics, 1997-12-01)
    We use Γ-convergence to prove existence of stable multiple-layer stationary solutions (stable patterns) to a reaction-diffusion 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 

    Sango, Mamadou (Texas State University, Department of Mathematics, 1997-11-29)
    We establish the completeness and the summability in the sense of Abel-Lidskij of the root vectors of a non-selfadjoint elliptic problem with an indefinite weight matrix and the angular distribution of its eigenvalues.

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