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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 Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations 

    Binding, Paul A.; Drabek, Pavel; Huang, Yin Xi (Texas State University, Department of Mathematics, 1997-01-30)
    We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem { −div (|∇u|p−2∇u) = λa(x)|u|p−2u + b(x)|u|γ−2u, x ∈ Ω, ∂u = 0, x ∈ ∂Ω , ∂n where Ω is a smooth ...
  • Positive Solutions and Nonlinear Multipoint Conjugate Eigenvalue Problems 

    Eloe, Paul W.; Henderson, Johnny (Texas State University, Department of Mathematics, 1997-12-19)
    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 

    Clark, M. R.; Lima, O. A. (Texas State University, Department of Mathematics, 1997-03-06)
    In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system utt − M ( |∇u|2dx)∆u + |u|ρu + θ = f Ω θt − ∆θ + ut = g where M is a positive real function, ...
  • Stability of a Linear Oscillator with Variable Parameters 

    Ignatyev, Alexander O. (Texas State University, Department of Mathematics, 1997-10-29)
    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 

    Drager, Lance D.; Layton, William (Texas State University, Department of Mathematics, 1997-12-19)
    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 

    Chen, Chao-Nien; Tzeng, Shyuh-yaur (Texas State University, Department of Mathematics, 1997-03-26)
    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 

    Carlson, Robert (Texas State University, Department of Mathematics, 1997-12-18)
    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 

    Grossinho, Maria do Rosario; Omari, Pierpaolo (Texas State University, Department of Mathematics, 1997-04-22)
    We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions. We assume that the primitive ...
  • Behaviour Near the Boundary for Solutions of Elasticity Systems 

    Domingos Cavalcanti, V. N. (Texas State University, Department of Mathematics, 1997-07-31)
    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 

    Khatskevich, Victor; Reich, Simeon; Shoikhet, David (Texas State University, Department of Mathematics, 1997-10-29)
    We characterize those holomorphic mappings which are the infinitesimal generators of semi-flows on bounded symmetric domains in complex Banach spaces.
  • Multiple Positive Solutions for Equations Involving Critical Sobolev Exponent in RN 

    Alves, C. O. (Texas State University, Department of Mathematics, 1997-08-19)
    This article concerns with the problem −div(|∇u|m−2∇u) = λhuq + um∗−1, in RN . Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of λ∗ > 0 such that there are at least two ...
  • Qualitative Behavior of Axial-Symmetric Solutions of Elliptic Free Boundary Problems 

    Acker, Andrew F.; Lancaster, Kirk E. (Texas State University, Department of Mathematics, 1997-01-08)
    A general free boundary problem in R3 is investigated for axial-symmetric solutions and qualitative geometric properties of the free boundary are compared to those of the fixed boundary for the axial and radial directions. ...
  • Nonlinear Weakly Elliptic 2X2 Systems of Variational Inequalities with Unilateral Obstacle Constraints 

    Adams, David R.; Nussenzveig Lopes, Helena J. (Texas State University, Department of Mathematics, 1997-10-31)
    We study 2X2 systems of variational inequalities which are only weakly elliptic; in particular, these systems are not necessarily monotone. The prototype differential operator is the (vector-valued) p-Laplacian. We prove, ...
  • Sub-Elliptic Boundary Value Problems for Quasilinear Elliptic Operators 

    Palagachev, Dian K.; Popivanov, Peter R. (Texas State University, Department of Mathematics, 1997-01-08)
    Classical solvability and uniqueness in the Ho¨lder space C2+α(Ω) is proved for the oblique derivative problem aij(x)Diju + b(x, u, Du) = 0 in Ω, ∂u/∂R = ϕ(x) on ∂Ω in the case when the vector field R(x) = (R1(x), ...
  • Asymptotic Instability of Nonlinear Differential Equations 

    Avis, Rafael; Naulin, Raul (Texas State University, Department of Mathematics, 1997-10-15)
    This article shows that the zero solution to the system xi = A(t)x + f(t, x), f(t, 0) = 0 is unstable. To show instability, we impose conditions on the nonlinear part f(t, x) and on the fundamental matrix of the linear ...
  • Nonexistence of Positive Singular Solutions for a Class of Semilinear Elliptic Systems 

    Yarur, Cecilia S. (Texas State University, Department of Mathematics, 1996-09-06)
    We study nonexistence and removability results for nonnegative sub- solutions to ∆u = a(x)vp ∆v = b(x)uq 1 in Ω ⊂ RN, N ≥ 3 , where p ≥ 1, q ≥ 1, pq > 1, and a and b are nonnegative functions. As a consequence ...
  • Lavrentiev Phenomenon in Microstructure Theory 

    Winter, Matthias (Texas State University, Department of Mathematics, 1996-08-22)
    A variational problem arising as a model in martensitic phase transformation including surface energy is studied. It explains the complex, multi-dimensional pattern of twin branching which is often observed in a martensitic ...
  • A Lower Bound for the Gradient of ∞-Harmonic Functions 

    Rosset, Edi (Texas State University, Department of Mathematics, 1996-02-06)
    We establish a lower bound for the gradient of the solution to infinity-Laplace equation in a strongly star-shaped annulus with capacity type boundary conditions. The proof involves properties of the radial derivative of ...
  • Radially Symmetric Solutions for a Class of Critical Exponent Elliptic Problems in RN 

    Alves, C. O.; de Morais Filho, D. C.; Souto, M. A. S. (Texas State University, Department of Mathematics, 1996-08-30)
    We give a method for obtaining radially symmetric solutions for the critical exponent problem ( −∆u + a(x)u = λuq + u2∗−1 in RN where, outside a ball centered at the origin, the non-negative function a is bounded ...
  • Weak Solutions to the One-dimensional Non-Isentropic Gas Dynamics by the Vanishing Viscosity Method 

    Ito, Kazufumi (Texas State University, Department of Mathematics, 1996-06-18)
    In this paper we consider the non-isentropic equations of gas dynamics with the entropy preserved. Equations are formulated so that the problem is reduced into the 2 × 2 system of conservation laws with a forcing term in ...

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