Existence and multiplicity of solutions for asymptotically linear Schrödinger–Kirchhoff equations

2015 ◽  
Vol 26 ◽  
pp. 191-198 ◽  
Author(s):  
Yue Wu ◽  
Shibo Liu
Keyword(s):  
Asymptotically Linear ◽  
Kirchhoff Equations ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-26
Author(s):  
Bo Zheng
Keyword(s):  
Nonlinear Analysis ◽  
Boundary Value Problems ◽  
Morse Theory ◽  
Boundary Value ◽  
Asymptotically Linear ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Linear Condition ◽  
Concrete Computation ◽  
Special Case

We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, some new conditions on the existence and multiplicity of solutions are obtained by combining some nonlinear analysis methods, such as Leray-Schauder principle and Morse theory. Our results are new even for the case of asymptotically linear.

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