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 Bifurcation of Sign-Changing Solutions for m-Point Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yulian An ◽  
Maoan Han
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Global Structure ◽  
Point Boundary ◽  
Multiplicity Results ◽  
Sign Changing Solutions

With the help of bifurcation techniques, some multiplicity results and global structure for sign-changing solutions of some m-point boundary value problems are obtained when the nonlinear term is sublinear at 0.

scholarly journals Existence of Nontrivial Solutions for Some Second-Order Multipoint Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Hongyu Li ◽  
Junting Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Theorems ◽  
Lattice Structure ◽  
Boundary Value ◽  
Second Order ◽  
Negative Solution ◽  
Nontrivial Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

By using fixed point theorems with lattice structure, the existence of negative solution and sign-changing solution for some second-order multipoint boundary value problems is obtained.

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 Effects of Nonlinearity on the Variational Iteration Solutions of Nonlinear Two-Point Boundary Value Problems with Comparison with Respect to Finite Element Analysis

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
MehmetTarık Atay ◽  
SafaBozkurt Coşkun
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Burger Equation ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Point Boundary ◽  
Element Analysis ◽  
Variational Iteration ◽  
Fine Mesh

Solution of a nonlinear two-point boundary value problem is studied using variational iteration method (VIM) considering its convergence behavior due to the changing nonlinearity effects in the equation. To achieve this, steady Burger equation is first solved by using finite element method (FEM) with a very fine mesh for the comparison of results obtained from VIM. Effect of the nonlinear term in the equation that is multiplied by a constant is taken into account for five different cases by changing the corresponding constant. Results have shown that VIM is a flexible, easy to apply, and promising method for the analysis of nonlinear two-point boundary value problems with the fact that the larger the effect of the nonlinear term of the equation, the slower the convergence rate when compared to FEM solutions.

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