scholarly journals Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Chengjun Yuan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Order Difference ◽  
Existence Of Positive Solutions

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equationsΔ4u(i−2)=λα(i)f(i,u(i)),i∈[2,T+2],u(0)=u(1)=0,u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone.

scholarly journals On the existence of positive solutions for generalized fractional boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Arjumand Seemab ◽  
Mujeeb Ur Rehman ◽  
Jehad Alzabut ◽  
Abdelouahed Hamdi
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Green Functions ◽  
Fractional Operators ◽  
Existence Of Positive Solutions ◽  
Different Types ◽  
Fractional Boundary Value Problems

AbstractThe existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.

scholarly journals Existence of Positive Solutions for Fourth-Order Boundary Value Problems with Sign-Changing Nonlinear Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xingfang Feng ◽  
Hanying Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

the existence of positive solutions for a fourth-order boundary value problem with a sign-changing nonlinear term is investigated. By using Krasnoselskii’s fixed point theorem, sufficient conditions that guarantee the existence of at least one positive solution are obtained. An example is presented to illustrate the application of our main results.

Singular boundary value problems for P-Laplacian-like equations

1997 ◽  
Vol 127 (5) ◽  
pp. 975-981 ◽  
Author(s):  
D. D. Hai ◽  
Seth F. Oppenheimer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Nonlinear Boundary Value Problems ◽  
Existence Of Positive Solutions

SynopsisWe consider the existence of positive solutions to a class of singular nonlinear boundary value problems for P-Laplacian-like equations. Our approach is based on the Schauder Fixed-Point Theorem.

scholarly journals Impulsive Antiperiodic Boundary Value Problems for Nonlinearqk-Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Lihong Zhang ◽  
Bashir Ahmad ◽  
Guotao Wang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Uniqueness Of Solutions

We show the existence and uniqueness of solutions for an antiperiodic boundary value problem of nonlinear impulsiveqk-difference equations by applying some well-known fixed point theorems. An example is presented to illustrate the main results.

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