Journals and Conference ProceedingsThe Journals and Conference Proceedings Collection includes publications reviewed and published by members of the university community and proceedings from conferences hosted by, or sponsored by, Texas State University.https://digital.library.txstate.edu/handle/10877/1362019-12-12T04:17:58Z2019-12-12T04:17:58ZSteady-state Bifurcations of the Three-dimensional Kolmogorov ProblemChen, Zhi-MinWang, Shouhonghttps://digital.library.txstate.edu/handle/10877/90582019-12-11T19:46:25Z2000-08-30T00:00:00ZSteady-state Bifurcations of the Three-dimensional Kolmogorov Problem
Chen, Zhi-Min; Wang, Shouhong
<p>This paper studies the spatially periodic incompressible fluid motion in ℝ3 excited by the external force k2 (sin kz,0,0) with k ≥ 2 an integer. This driving force gives rise to the existence of the unidirectional basic steady flow u0 = (sin kz,0,0) for any Reynolds number. It is shown in Theorem 1.1 that there exist a number of critical Reynolds numbers such that u0 bifurcates into either 4 or 8 or 16 different steady states, when the Reynolds number increases across each of such numbers.</p>
<p>Thanks to the Rabinowitz global bifurcation theorem, all of the bifurcation solutions are extended to global branches for λ ∈ (0,∞). Moreover we prove that when λ passes each critical value, a) all the corresponding global branches do not intersect with the trivial branch (u0,λ), and b) some of them never intersect each other; see theorem 1.2.</p>
2000-08-30T00:00:00ZUniform Exponential Stability of Linear Almost Periodic Systems in Banach SpacesCheban, David N.https://digital.library.txstate.edu/handle/10877/90572019-12-11T19:23:26Z2000-04-17T00:00:00ZUniform Exponential Stability of Linear Almost Periodic Systems in Banach Spaces
Cheban, David N.
This article is devoted to the study linear non-autonomous dynamical systems possessing the property of uniform exponential stability. We prove that if the Cauchy operator of these systems possesses a certain compactness property, then the uniform asymptotic stability implies the uniform exponential stability. For recurrent (almost periodic) systems this result is precised. We also show application for different classes of linear evolution equations: ordinary linear differential equations in a Banach space, retarded and neutral functional differential equations, and some classes of evolution partial differential equations.
2000-04-17T00:00:00ZNonclassical Sturm-Liouville Problems and Schrodinger Operators on Radial TreesCarlson, Roberthttps://digital.library.txstate.edu/handle/10877/90562019-12-11T19:18:01Z2000-11-28T00:00:00ZNonclassical Sturm-Liouville Problems and Schrodinger Operators on Radial Trees
Carlson, Robert
Schrodinger operators on graphs with weighted edges may be defined using possibly infinite systems of ordinary differential operators. This work mainly considers radial trees, whose branching and edge lengths depend only on the distance from the root vertex. The analysis of operators with radial coefficients on radial trees is reduced, by a method analogous to separation of variables, to nonclassical boundary-value problems on the line with interior point conditions. This reduction is used to study self adjoint problems requiring boundary conditions `at infinity'.
2000-11-28T00:00:00ZPositive Solutions to a Second Order Multi-point Boundary-value ProblemCao, DaominMa, Ruyunhttps://digital.library.txstate.edu/handle/10877/90552019-12-11T18:45:34Z2000-10-30T00:00:00ZPositive Solutions to a Second Order Multi-point Boundary-value Problem
Cao, Daomin; Ma, Ruyun
We prove the existence of positive solutions to the boundary-value problem u" + λα(t) ƒ (u,u') = 0 u(0) = 0, u(1) = m-2 ∑ i=1 αiu(↋i), where α is a continuous function that may change sign on [0,1], ƒ is a continuous function with ƒ (0,0) > 0, and λ is a samll positive constant. For finding solutions we use the Leray-Schauder fixed point theorem.
2000-10-30T00:00:00Z