scholarly journals New existence and multiplicity of homoclinic solutions for second order non-autonomous systems

2014 ◽  
pp. 1-18 ◽  
Author(s):  
Huiwen Chen ◽  
Zhimin He
Keyword(s):  
Autonomous Systems ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Existence And Multiplicity

scholarly journals Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Qiongfen Zhang ◽  
Yuan Li
Keyword(s):  
Continuous Function ◽  
Mountain Pass Theorem ◽  
Weighted Sobolev Space ◽  
Point Theory ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Nonautonomous Systems ◽  
Symmetric Mountain Pass Theorem ◽  
Existence And Multiplicity

This paper is concerned with the following nonlinear second-order nonautonomous problem:ü(t)+q(t)u̇(t)-∇K(t,u(t))+∇W(t,u(t))=0, wheret∈R,u∈RN, andK,W∈C1(R×RN,R)are not periodic intandq:R→Ris a continuous function andQ(t)=∫0t‍q(s)dswithlim|t|→+∞⁡Q(t)=+∞. The existence and multiplicity of fast homoclinic solutions are established by using Mountain Pass Theorem and Symmetric Mountain Pass Theorem in critical point theory.

Homoclinic solutions of some second order non-autonomous systems

2009 ◽  
Vol 71 (11) ◽  
pp. 5790-5798 ◽  
Author(s):  
Ziheng Zhang ◽  
Rong Yuan
Keyword(s):  
Autonomous Systems ◽  
Second Order ◽  
Homoclinic Solutions

scholarly journals Data assimilation for massive autonomous systems based on a second-order adjoint method

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
Shin-ichi Ito ◽  
Hiromichi Nagao ◽  
Akinori Yamanaka ◽  
Yuhki Tsukada ◽  
Toshiyuki Koyama ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Adjoint Method ◽  
Autonomous Systems ◽  
Second Order
Sign in / Sign up

Export Citation Format

Share Document