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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Recent Submissions

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. 
Multiple Positive Solutions for Equations Involving Critical Sobolev Exponent in RN
(Texas State University, Department of Mathematics, 19970819)This article concerns with the problem −div(∇um−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 AxialSymmetric Solutions of Elliptic Free Boundary Problems
(Texas State University, Department of Mathematics, 19970108)A general free boundary problem in R3 is investigated for axialsymmetric 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
(Texas State University, Department of Mathematics, 19971031)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 (vectorvalued) pLaplacian. We prove, ... 
SubElliptic Boundary Value Problems for Quasilinear Elliptic Operators
(Texas State University, Department of Mathematics, 19970108)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
(Texas State University, Department of Mathematics, 19971015)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
(Texas State University, Department of Mathematics, 19960906)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
(Texas State University, Department of Mathematics, 19960822)A variational problem arising as a model in martensitic phase transformation including surface energy is studied. It explains the complex, multidimensional pattern of twin branching which is often observed in a martensitic ... 
A Lower Bound for the Gradient of ∞Harmonic Functions
(Texas State University, Department of Mathematics, 19960206)We establish a lower bound for the gradient of the solution to infinityLaplace equation in a strongly starshaped 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
(Texas State University, Department of Mathematics, 19960830)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 nonnegative function a is bounded ... 
Weak Solutions to the Onedimensional NonIsentropic Gas Dynamics by the Vanishing Viscosity Method
(Texas State University, Department of Mathematics, 19960618)In this paper we consider the nonisentropic 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 ...