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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.

EJDE Journal Website: http://ejde.math.txstate.edu/

### Recent Submissions

• #### Partial Exact Controllability for the Linear Thermo-Viscoelastic Model ﻿

(Texas State University, Department of Mathematics, 1998-06-20)
The problem of partial exact controllability for linear thermo-viscoelasticity is considered. Using classical multiplier techniques, a boundary observability inequality is established under smallness restrictions on coupling ...
• #### On Multi-Lump Solutions to the Non-Linear Schrodinger Equation ﻿

(Texas State University, Department of Mathematics, 1998-11-15)
We present a new approach to proving the existence of semi-classical bound states of the non-linear Schrodinger equation which are concentrated near a finite set of non-degenerate critical points of the potential function. ...
• #### On Tykhonov's Theorem for Convergence of Solutions of Slow and Fast Systems ﻿

(Texas State University, Department of Mathematics, 1998-07-09)
Slow and fast systems gain their special structure from the presence of two time scales. Their analysis is achieved with the help of Singular Perturbation Theory. The fundamental tool is Tykhonov's theorem which describes ...
• #### Existence and Regularity Results for the Gradient Flow for p-Harmonic Maps ﻿

(Texas State University, Department of Mathematics, 1998-12-21)
We establish existence and regularity for a solution of the evolution problem associated to p-harmonic maps if the target manifold has a nonpositive sectional curvature.
• #### Stability of Strong Detonation Waves and Rates of Convergence ﻿

(Texas State University, Department of Mathematics, 1998-03-18)
In this article, we prove stability of strong detonation waves and find their rate of convergence for a combustion model. Our results read as follows: I) There exists a global solution that converges exponentially in time ...
• #### Instability of Discrete Systems ﻿

(Texas State University, Department of Mathematics, 1998-12-08)
In this paper, we give criteria for instability and asymptotic instability for the null solution to the non-autonomous system of difference equations y(t + 1) = A(t)y(t) + f(t,y(t)), f(t,0) = 0, when the system x(t + 1) ...
• #### Existence and Multiplicity of Solutions to a p-Laplacian Equation with Nonlinear Boundary Condition ﻿

(Texas State University, Department of Mathematics, 1998-04-10)
We study the nonlinear elliptic boundary value problem Au = f(x,u) in Ω, Bu = g(x,u) on ∂Ω, where A is an operator of p-Laplacian type, Ω is an unbounded domain in ℝ(N) with non-compact boundary, and f and g are subcritical ...
• #### Symmetry and Convexity of Level Sets of Solutions to the Infinity Laplace's Equation ﻿

(Texas State University, Department of Mathematics, 1998-12-09)
We consider the Dirichlet problem -Δ∞u = f(u) in Ω, u = 0 on ∂Ω, where Δ∞u = u(x)(i), u(x)(j), u(x)(i)(x)j) and f is a nonnegative continuous function. We investigate whether the solutions to this equation inherit geometrical ...
• #### Branching of Periodic Orbits from Kukles Isochrones ﻿

(Texas State University, Department of Mathematics, 1998-05-13)
We study local bifurcations of limit cycles from isochronous (or linearizable) centers. The isochronicity has been determined using the method of Darboux linearization, which provides a birational linearization for the ...
• #### Stationary Solutions for Generalized Boussinesq Models in Exterior Domains ﻿

(Texas State University, Department of Mathematics, 1998-10-01)
We establish the existence of a stationary weak solution of a generalized Boussinesq model for thermally driven convection in exterior domains. We use the fact that the exterior domain can be approximated by interior domains.
• #### Quasi-Geostrophic Type Equations with Weak Initial Data ﻿

(Texas State University, Department of Mathematics, 1998-06-12)
We study the initial value problem for the quasi-geostrophic type equations ∂θ / ∂t + u • ∇θ + (-Δ)(λ)θ = 0, on ℝ(n) x (0, ∞), θ(x,0) = θ(0)(x), x ∈ ℝ(n), where λ(0 ≤ λ ≤ 1) is a fixed parameter and u = (u(j)) is divergence ...
• #### Pressure Conditions for the Local Regularity of Solutions of the Navier-Stokes Equations ﻿

(Texas State University, Department of Mathematics, 1998-05-13)
We obtain a relationship between the integrability of the pressure gradient and the the integrability of the velocity for local solutions of the Navier--Stokes equations with finite energy. In particular, we show that if ...
• #### On Reaction-Diffusion Systems ﻿

(Texas State University, Department of Mathematics, 1998-10-09)
We consider reaction-diffusion systems which are strongly coupled. we prove that they generate analytic semigroups, find a characterization for the spectrum of the generator, and present some examples.
• #### Optimizing Chemotherapy in an HIV Model ﻿

(Texas State University, Department of Mathematics, 1998-12-04)
We examine an ordinary differential system modeling the interaction of the HIV virus and the immune system of the human body. The optimal control represents a percentage effect the chemotherapy has on the interaction of ...
• #### A Hyperbolic Problem with Nonlinear Second-Order Boundary Damping ﻿

(Texas State University, Department of Mathematics, 1998-10-30)
The initial boundary value problem for the wave equation with nonlinear second-order dissipative boundary conditions is considered. Existence and uniqueness of global generalized solutions are proved.
• #### A Scaled Characteristics Method for the Asymptotic Solution of Weakly Nonlinear Wave Equations ﻿

(Texas State University, Department of Mathematics, 1998-01-31)
We formulate a multi-scale perturbation technique to asymptotically solve weakly nonlinear hyperbolic equations. The method is based on a set of scaled characteristic coordinates. We show that this technique leads to a ...
• #### Exponentially Slow Traveling Waves on a Finite Interval for Burgers' Type Equation ﻿

(Texas State University, Department of Mathematics, 1998-11-20)
In this paper we study for small positive $\epsilon$ the slow motion of the solution for evolution equations of Burgers' type with small diffusion, ut = Euxx + f (u) ux , u(x, 0) = u0(x), u(±1, t) = ±1, (*) on the ...
• #### Existence of Periodic Solutions for a Semilinear Ordinary Differential Equation ﻿

(Texas State University, Department of Mathematics, 1998-11-20)
Dancer [3] found a necessary and sufficient condition for the existence of periodic solutions to the equation x¨ + g1 (x˙) + g0(x) = f (t) His condition is based on a functional that depends on the solution to the ...
• #### Invariance of Poincare-Lyapunov Polynomials Under the Group of Rotations ﻿

(Texas State University, Department of Mathematics, 1998-10-09)
We show that the Poincare-Lyapunov polynomials at a focus of a family of real polynomial vector fields of degree $n$ on the plane are invariant under the group of rotations. Furthermore, we show that under the multiplicative ...
• #### Complex Continued Fractions with Restricted Entries ﻿

(Texas State University, Department of Mathematics, 1998-10-19)
We study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted ...