Infinitely many solutions for nonlinear periodic boundary value problem with impulses

2016 ◽  
Vol 111 (4) ◽  
pp. 1093-1103
Author(s):  
Weibing Wang
Keyword(s):  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Infinitely Many Solutions

scholarly journals Infinitely Many Solutions for a Generalized Periodic Boundary Value Problem without the Evenness Assumption

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaodong Gu ◽  
Mingliang Song
Keyword(s):  
Boundary Value Problem ◽  
Critical Point ◽  
Hamiltonian Systems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Periodic Boundary Value Problem ◽  
Infinitely Many Solutions ◽  
Critical Point Theorem ◽  
Second Order Hamiltonian Systems

In this paper, we investigate infinitely many solutions for the generalized periodic boundary value problem −x″−B0tx+B1tx=λ∇xVt,xa.e.t∈0,1,x1=Mx0,x′1=Nx′0 under the potential function Vt,x without the evenness assumption and obtain two new existence results by the multiple critical point theorem. Meanwhile, we give two corollaries for the periodic solutions of second-order Hamiltonian systems and an example that illustrates our results.

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