scholarly journals Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator

2020 ◽  
Vol 40 (4) ◽  
pp. 405-425 ◽  
Author(s):  
Pablo Amster ◽  
Mariel Paula Kuna ◽  
Dionicio Pastor Santos
Keyword(s):  
Boundary Value Problems ◽  
Time Scales ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a \(\varphi\)-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete \(p\)-Laplacian as well as those for boundary value problems on time scales.

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.

Existence and Multiple Solutions for Higher Order Difference Dirichlet Boundary Value Problems

2018 ◽  
Vol 19 (5) ◽  
pp. 539-544
Author(s):  
Lianwu Yang
Keyword(s):  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Higher Order ◽  
Nonlinear Difference Equation ◽  
Linking Theorem ◽  
Order Difference ◽  
Existence And Multiplicity

AbstractIn this paper, a higher order nonlinear difference equation is considered. By using the critical point theory, we obtain the existence and multiplicity for solutions of difference Dirichlet boundary value problems and give some new results. The proof is based on the variational methods and linking theorem.

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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