Absolutely continuous spectrum of fourth order difference equations

2014 ◽  
Vol 288 (8-9) ◽  
pp. 1009-1027
Author(s):  
Fredrick Oluoch Nyamwala
Keyword(s):  
Continuous Spectrum ◽  
Fourth Order ◽  
Difference Equations ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
Order Difference

scholarly journals Multiple solutions of fourth-order difference equations with different boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuhua Long ◽  
Shaohong Wang ◽  
Jiali Chen
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Difference Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Dirichlet Boundary Conditions ◽  
Invariant Sets ◽  
Mountain Pass Lemma ◽  
Order Difference

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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