Journals and Conference Proceedings
https://digital.library.txstate.edu/handle/10877/136
The 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.2019-10-13T02:48:42ZFredholm Linear Operators Associated with Ordinary Differential Equations on Noncompact Intervals
https://digital.library.txstate.edu/handle/10877/8648
Fredholm Linear Operators Associated with Ordinary Differential Equations on Noncompact Intervals
Cecchi, Mariella; Furi, Massimo; Marini, Mauro; Pera, Maria Patrizia
In the noncompact interval J = [α, ∞) we consider a linear problem of the form Lx = y, x ∈ S, where L is a first order differential operator, y a locally summable function in J, and S a subspace of the Fréchet space of the locally absolutely continuous functions in J. In the general case, the restriction of L to S is not a Fredholm operator. However, we show that, under suitable assumptions, S and L(S) can be regarded as subspaces of two quite natural spaces in such a way that L becomes a Fredholm operator between them. Then, the solvability of the problem will be reduced to the task of finding linear functionals defined in a convenient subspace of L1(loc) (J, Rn) whose “kernel intersection” coincides with L(S).
We will prove that, for a large class of “boundary sets” S, such functionals can be obtained by reducing the analysis to the case when the function y has compact support. Moreover, by adding a suitable stronger topological assumption on S, the functionals can be represented in an integral form. Some examples illustrating our results are given as well.
1999-10-31T00:00:00ZOn the Dirichlet Problem for Quasilinear Elliptic Second Order Equations with Triple Degeneracy and Singularity in a Domain with a Boundary Conical Point
https://digital.library.txstate.edu/handle/10877/8647
On the Dirichlet Problem for Quasilinear Elliptic Second Order Equations with Triple Degeneracy and Singularity in a Domain with a Boundary Conical Point
Borsuk, Michail; Portnyagin, Dmitriy
In this article we prove boundedness and Holder continuity of weak solutions to the Dirichlet problem for a second order quasilinear elliptic equation with triple degeneracy and singularity. In particular, we study equations of the form
- d/dxi (|x|τ|u|q|∇u|m−2uxt) + α0|x|τ/(x2 n-1 + x2n)m/2 u|u|q+m-2 - µ|x|τ u|u|q-2|∇u|m =
</br>
= fo(x) - ∂fi / ∂xi,
with α0 ≥ 0, q ≥ 0, 0 ≤ µ < 1, 1 < m ≤ n, and τ > m − n in a domain with a boundary conical point. We obtain the exact Hölder exponent of the solution near the conical point.
1999-06-24T00:00:00ZReligion, Freedom, and Prosperity in Oklahoma Country Music
https://digital.library.txstate.edu/handle/10877/8634
Religion, Freedom, and Prosperity in Oklahoma Country Music
Wenzel, Nikolai G.
No abstract prepared.
2018-01-01T00:00:00ZReviews [2018]
https://digital.library.txstate.edu/handle/10877/8633
Reviews [2018]
Riddle, Kelsey; Peoples, Curtis L.
Review of "Armadillo World Headquarters: A Memoir," by Eddie Wilson with Jesse Sublett, and "Delbert McClinton: One of the Fortunate Few," by Diana Finlay Hendricks.
2018-01-01T00:00:00Z