摘要：
In this paper, solutions of a Novikov equation are discussed based on the bifurcation method of dynamical systems. Through establishing a Hamiltonian function, the existence of a smooth soliton solution and a periodic cuspon solution are established for the corresponding traveling wave system of the Novikov equation. Numerical results are carried out to illustrate the feasibility of the main results. All these theories can be seen to fill the gap of the literatures Li (2014) and Pan and Li (2016). (C) 2020 Elsevier Ltd. All rights reserved.
期刊：
BOUNDARY VALUE PROBLEMS,2019年2019(1):1-15 ISSN：1687-2762
通讯作者：
Li, Lin
作者机构：
[Li, Lin; Ouyang, Zigen; Huang, Qizheng] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
通讯机构：
[Li, Lin] U;Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
关键词：
Laminar flow;Expanding and contracting walls;Singular perturbation method;Exponentially small terms
摘要：
This paper is concerned with asymptotic solutions of a nonlinear boundary value problem which arises from laminar flow in a uniformly porous channel with expanding or contracting walls. For values of the wall suction Reynolds number, multiple solutions are observed. A method involving the inclusion of exponentially small terms in a perturbation series is mainly considered to obtain two of the solutions analytically. In addition, numerical solutions presented for each case agree well with asymptotic solutions, which illustrates that the asymptotic solutions constructed in this paper are more reliable.
作者机构：
[Ouyang, Zigen; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Zhang, Jianjun] Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China.;[Zhang, Jianjun] Univ Insubria, Dipartimento Sci & Alta Tecnol, Via GB Vico 46, I-21100 Varese, Italy.
通讯机构：
[Zhang, Jianjun] C;[Zhang, Jianjun] U;Chongqing Jiaotong Univ, Coll Math & Stat, Chongqing 400074, Peoples R China.;Univ Insubria, Dipartimento Sci & Alta Tecnol, Via GB Vico 46, I-21100 Varese, Italy.
关键词：
gauged Schrodinger equations;sign-changing solutions;invariant sets of descending flow
期刊：
Advances in Difference Equations,2018年2018(1):1-18 ISSN：1687-1839
通讯作者：
Liu, Hongliang
作者机构：
[Xiao, Qizhen; Liu, Hongliang; Ouyang, Zigen] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
通讯机构：
[Liu, Hongliang] U;Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
关键词：
Biharmonic equation;Variational methods;High energy solutions;Concentration of solutions
摘要：
We consider the following nonlinear biharmonic equations:
$$ \Delta^{2} u-\Delta u+ V_{\lambda }(x)u=f(x,u),\quad \text{in } \mathbb{R}^{N}, $$
where
$V_{\lambda }(x)$
is allowed to be sign-changing and f is an indefinite function. Under some suitable assumptions, the existence of nontrivial solutions and the high energy solutions are obtained by using variational methods. Moreover, the phenomenon of concentration of solutions is explored. The results extend the main conclusions in recent literature.
期刊：
BOUNDARY VALUE PROBLEMS,2018年2018(1):1-14 ISSN：1687-2762
通讯作者：
Ouyang, Zigen
作者机构：
[Zhou, Chengfang; Ouyang, Zigen] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
通讯机构：
[Ouyang, Zigen] U;Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
关键词：
Biharmonic equations;Singular potential;Morse theory;Critical groups
摘要：
In this paper, we study a class of biharmonic equations with a singular potential in
$\mathbb{R}^{N}$
. Under appropriate assumptions on the nonlinearity, we establish some existence results via the Morse theory and variational methods. We significantly extend and complement some results from the previous literature.
期刊：
TAIWANESE JOURNAL OF MATHEMATICS,2017年21(2):403-428 ISSN：1027-5487
通讯作者：
Chen, Huiwen
作者机构：
[Chen, Huiwen; Ouyang, Zigen] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[He, Zhimin] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Li, Jianli] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China.
通讯机构：
[Chen, Huiwen] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Homoclinic solutions;Discrete Hamiltonian systems;Asymptotically quadratic;Supquadratic;Critical point theory;Variational methods
摘要：
In this paper, we deal with the second order discrete Hamiltonian system Delta[p(n) Delta u (n - 1)]- L(n)u(n) + Delta W(n; u ( n)) = 0, where L : Z -> R (NxN) is positive de fi nite for su ffi ciently large vertical bar n vertical bar epsilon Z and W(n; x) is inde fi nite sign. By using critical point theory, we establish some new criteria to guarantee that the above system has in fi nitely many nontrivial homoclinic solutions under the assumption that W(n; x) is asymptotically quadratic and supquadratic, respectively. Our results generalize and improve some existing results in the literature.
作者机构：
[Yang, Liu] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China.;[Ouyang, Zigen; Liu, Zhisu] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, Zhisu] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Multiplicity;Kirchhoff type equation;Critical growth
摘要：
In this paper, we study the following Kirchhoff type equation with critical growth {-(a + b integral(Omega) vertical bar del u vertical bar(2)dx) del u = lambda u + mu vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0 on partial derivative Omega, where a > 0, b >= 0 and Omega is a smooth bounded domain in R-3. When the real parameter mu is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter lambda belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator -Delta. (C) 2016 Elsevier Ltd. All rights reserved.
