Existence of nontrivial solutions for discrete nonlinear two point boundary value problems

2006 ◽  
Vol 180 (1) ◽  
pp. 318-329 ◽  
Author(s):  
Liqun Jiang ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Nontrivial Solutions

Solutions of second order multi-point boundary value problems

2008 ◽  
Vol 145 (2) ◽  
pp. 489-510 ◽  
Author(s):  
JOHN R. GRAEF ◽  
LINGJU KONG
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Linear Integral ◽  
The Relationship

AbstractWe consider classes of second order boundary value problems with a nonlinearity f(t, x) in the equations and subject to a multi-point boundary condition. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. The symmetry of solutions is also studied. Conditions are determined by the relationship between the behavior of the quotient f(t, x)/x for x near 0 and ∞ and the largest positive eigenvalue of a related linear integral operator. Our analysis mainly relies on the topological degree and fixed point index theories.

scholarly journals Existence of Nontrivial Solutions for Unilaterally Asymptotically Linear Three-Point Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hongyu Li
Keyword(s):  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Lattice Structure ◽  
Boundary Value ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Asymptotically Linear ◽  
Sign Changing Solutions ◽  
Ordered Banach Spaces

Using fixed point theorems in ordered Banach spaces with the lattice structure, we consider the existence of nontrivial solutions under the condition that the nonlinear term can change sign and study the existence of sign-changing solutions for some second order three-point boundary value problems. Our results improve and generalize on those in the literatures.

scholarly journals Weak Nontrivial Solutions to Discrete Nonlinear Two-Point Boundary-Value Problems of Kirchhoff Type

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Rodrigue SANOU ◽  
◽  
Idrissa IBRANGO ◽  
Blaise KONÉ ◽  
◽  
...  
Keyword(s):  
Variational Principle ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Existence Results ◽  
Mountain Pass ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Kirchhoff Type

"We prove the existence of at least one weak nontrivial solutions for a discrete nonlinear two-point boundary-value problems of Kirchhoff type. The main existence results are obtained by using the technique of geometric mountain pass and the Ekelands variational principle."

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