scholarly journals On a fixed point index method for the analysis of the asymptotic behavior and boundary value problems of infinite dimensional dynamical systems and processes

1984 ◽  
Vol 52 (2) ◽  
pp. 162-174
Author(s):  
A.F Izé
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Point Index ◽  
Index Method ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems

scholarly journals A Generalization of Mahadevan's Version of the Krein-Rutman Theorem and Applications top-Laplacian Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yujun Cui ◽  
Jingxian Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Point Index ◽  
Homogeneous Operator ◽  
Existence Of Positive Solutions ◽  
Positive Eigenfunction ◽  
Homogeneous Operators

We will present a generalization of Mahadevan’s version of the Krein-Rutman theorem for a compact, positively 1-homogeneous operator on a Banach space having the properties of being increasing with respect to a conePand such that there is a nonzerou∈P∖{θ}−Pfor whichMTpu≥ufor some positive constantMand some positive integerp. Moreover, we give some new results on the uniqueness of positive eigenvalue with positive eigenfunction and computation of the fixed point index. As applications, the existence of positive solutions forp-Laplacian boundary-value problems is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.

UNIVERSAL PHENOMENA IN SOME INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

1995 ◽  
Vol 05 (05) ◽  
pp. 1419-1425 ◽  
Author(s):  
A. N. SHARKOVSKY
Keyword(s):  
Dynamical Systems ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
One Dimensional ◽  
Partial Derivatives ◽  
Infinite Dimensional ◽  
Qualitative And Quantitative ◽  
Infinite Dimensional Dynamical Systems

Qualitative and quantitative "universalities" known for one-dimensional dynamical systems are transferred to some infinite-dimensional dynamical systems given by difference and differential-difference equations, and also by boundary value problems for equations with partial derivatives.

Positive Solutions for Nonlinear Lidstone Boundary Value Problems

2013 ◽  
Vol 313-314 ◽  
pp. 1201-1204 ◽  
Author(s):  
Lei Wang ◽  
Li Li
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Existence Result ◽  
Boundary Value ◽  
Index Theorem ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem

In this paper, we consider the existence of positive solutions for nonlinear Lidstone boundary value problems. An new existence result is obtained by applying the fixed point index theorem.

scholarly journals Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jian-Ping Sun ◽  
Xue-Mei Yang ◽  
Ya-Hong Zhao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Main Tool ◽  
Point Boundary ◽  
Point Index ◽  
Third Order

We are concerned with the following system of third-order three-point boundary value problems:u′′′(t)+f(t,v(t))=0,t∈(0,1),v′′′(t)+g(t,u(t))=0,t∈(0,1),u(0)=u′′(0)=0,u′(1)=αu(η),v(0)=v′′(0)=0, andv′(1)=αv(η), where0<η<1and0<α<1/η. By imposing some suitable conditions onfandg, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.

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.

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