The existence and multiplicity of solutions of three-pointp-Laplacian boundary value problems with one-sided Nagumo condition

2007 ◽  
Vol 24 (1-2) ◽  
pp. 209-220
Author(s):  
Jianjun Zhang ◽  
Wenbin Liu ◽  
Jinbo Ni ◽  
Taiyong Chen
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Multiplicity Of Solutions ◽  
Nagumo Condition ◽  
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.

scholarly journals Some remarks on nonlinear discrete boundary value problems

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Marek Galewski ◽  
Joanna Smejda
Keyword(s):  
Nonlinear System ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Monotonicity Results

AbstractUsing critical point theory and some monotonicity results we consider the existence and multiplicity of solutions to nonlinear discrete boundary value problems represented as a nonlinear system

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