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https://digital.library.txstate.edu/handle/10877/1
Research, creative, and scholarly works created by the university community organized by department.2023-06-07T02:35:30ZExistence of two positive solutions for indefinite Kirchhoff equations in R^3
https://digital.library.txstate.edu/handle/10877/16909
Existence of two positive solutions for indefinite Kirchhoff equations in R^3
Ding, Ling; Meng, Yi-Jie; Xiao, Shi-Wu; Zhang, Jin-Ling
In this article we study the Kirchhoff type equation
-(1 + b ∫ℝ3 |∇u|2dx) ∆u + u = k(x) ƒ(u) + λh(x)u, x ∈ ℝ3,
u ∈ H1(ℝ3),
involving a linear part -∆u + u - λh(x)u which is coercive if 0 < λ < λ1(h)
and is noncoercive if λ > λ1(h), a nonlocal nonlinear term -b ∫ℝ3 |∇u|2dx∆u
and a sign-changing nonlinearity of the form k(x) ƒ(s), where b > 0, λ > 0 is a real
parameter and λ1(h) is the first eigenvalue of -∆u + u = λh(x)u. Under suitable assumptions on ƒ and h, we obtain positives solution for λ ∈ (0, λ1(h)) and two positive solutions with a condition on k.
2016-01-25T00:00:00ZAnalytic smoothing effect for the cubic hyperbolic Schrödinger equation in two space dimensions
https://digital.library.txstate.edu/handle/10877/16908
Analytic smoothing effect for the cubic hyperbolic Schrödinger equation in two space dimensions
Hoshino, Gaku; Ozawa, Tohru
We study the Cauchy problem for the cubic hyperbolic Schrödinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.
2016-01-25T00:00:00ZMorrey estimates for subelliptic p-Laplace type systems with VMO coefficients in Carnot groups
https://digital.library.txstate.edu/handle/10877/16907
Morrey estimates for subelliptic p-Laplace type systems with VMO coefficients in Carnot groups
Yu, Haiyan; Zheng, Shenzhou
In this article, we study estimates in Morrey spaces to the horizontal gradient of weak solutions for a class of quasilinear sub-elliptic systems of p-Laplace type with VMO coefficients under the controllable growth over Carnot group if p is not too far from 2. We also show a local Holder continuity with an optimal exponent to the solutions.
2016-01-21T00:00:00ZEntire functions that share a small function with their difference operators
https://digital.library.txstate.edu/handle/10877/16906
Entire functions that share a small function with their difference operators
El Farissi, Abdallah; Latreuch, Zinelaabidine; Belaidi, Benharrat; Asiri, Asim
In this article, we study the uniqueness of entire functions that share small functions of finite order with their difference operators. In particular, we give a generalization of results in [3,4,13].
2016-01-21T00:00:00Z