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.2022-01-18T07:50:10ZCritical second-order elliptic equation with zero Dirichlet boundary condition in four dimensions
https://digital.library.txstate.edu/handle/10877/15116
Critical second-order elliptic equation with zero Dirichlet boundary condition in four dimensions
Boucheche, Zakaria; Chtioui, Hichem; Hajaiej, Hichem
We are concerned with the nonlinear critical problem -∆u = K(x)u<sup>3</sup>, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain of ℝ<sup>4</sup>. Under the assumption that K is strictly decreasing in the outward normal direction on ∂Ω and degenerate at its critical points for an order β ∈ (1, 4), we provide a complete description of the lack of compactness of the associated variational problem and we prove an existence result of Bahri-Coron type.
2018-03-02T00:00:00ZMultiple state optimal design problems with random perturbation
https://digital.library.txstate.edu/handle/10877/15115
Multiple state optimal design problems with random perturbation
Vrdoljak, Marko
A multiple state optimal design problem with presence of uncertainty on the right-hand side is considered, in the context of stationary diffusion with two isotropic phases. A similar problem with one state equation has already been considered by Buttazzo and Maestre (2011). We shall address the question of relaxation by the homogenization method and necessary conditions of optimality. The case of discrete probability space leads to another multiple state problem (possibly with an infinite number of states), which could be treated by similar techniques to those presented in Allaire (2002) and Vrdoljak (2010). The relaxation can be expressed in a simpler form for problems with spherical symmetry in the case of minimization (or maximization) of averaged energy, and we present an example which can be solved explicitly.
2018-03-02T00:00:00ZGradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities
https://digital.library.txstate.edu/handle/10877/15114
Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities
Liang, Shuang; Zheng, Shenzhou
We prove a global Orlicz estimate for the gradient of weak solutions to a class of nonlinear obstacle problems with partially regular nonlinearities in nonsmooth domains. It is assumed that the nonlinearities are merely measurable in one spatial variable and have sufficiently small BMO semi-norm in the other variables, and the boundary of underlying domain is Reifenberg flat.
2018-03-01T00:00:00ZStability of traveling wavefronts for a three-component Lotka-Volterra competition system on a lattice
https://digital.library.txstate.edu/handle/10877/15113
Stability of traveling wavefronts for a three-component Lotka-Volterra competition system on a lattice
Su, Tao; Zhang, Guo-Bao
This article concerns the stability of traveling wavefronts for a three-component Lotka-Volterra competition system on a lattice. By means of the weighted energy method and the comparison principle, it is proved that the traveling wavefronts with large speed are exponentially asymptotically stable, when the initial perturbation around the traveling wavefronts decays exponentially as j + ct → -∞, where j ∈ ℤ, t > 0 and c > 0, but the initial perturbation can be arbitrarily large on other locations.
2018-03-01T00:00:00Z