scholarly journals HOMOCLINIC SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS WITH SUPERLINEAR NONLINEARITIES

2018 ◽  
Vol 8 (1) ◽  
pp. 66-80
Author(s):  
Ziheng Zhang ◽  
◽  
Zhisu Liu ◽  
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Homoclinic Solutions

scholarly journals Infinitely Many Homoclinic Solutions for Nonperiodic Fourth Order Differential Equations with General Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Liu Yang
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Point Theory ◽  
Homoclinic Solutions

We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.

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