scholarly journals Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractionalq-Derivatives Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yulin Zhao ◽  
Guobing Ye ◽  
Haibo Chen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Index Theorem ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fixed Point Index Theorem

By using the fixed point index theorem, this paper investigates a class of singular semipositone integral boundary value problem for fractionalq-derivatives equations and obtains sufficient conditions for the existence of at least two and at least three positive solutions. Further, an example is given to illustrate the applications of our main results.

Multiple positive solutions of nonlinear fractional differential equations with integral boundary value conditions

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Wei Sun ◽  
Youyu Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Fractional Differential

AbstractIn this paper, we consider the multiplicity of positive solutions for a class of nonlinear boundary-value problem of fractional differential equations with integral boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to the integral boundary value problem.

scholarly journals Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem

2016 ◽  
Vol 54 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Slimane Benaicha ◽  
Faouzi Haddouchi
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Existence Of Positive Solutions

Abstract In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.

scholarly journals Existence of Positive Solutions to Singular φ-Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 420 ◽  
Author(s):  
Jeongmi Jeong ◽  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Index Theorem ◽  
Multiple Positive Solutions ◽  
Nonlocal Boundary Value Problems ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem

In this paper, using a fixed point index theorem on a cone, we present some existence results for one or multiple positive solutions to φ -Laplacian nonlocal boundary value problems when φ is a sup-multiplicative-like function and the nonlinearity may not satisfy the L 1 -Carath e ´ odory condition.

scholarly journals Positive Solution of Fourth-Order Integral Boundary Value Problem with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Guoqing Chai
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Fourth Order ◽  
Boundary Value ◽  
Index Theorem ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Operator Spectrum ◽  
Fixed Point Index Theorem ◽  
Two Parameters

The author investigates the fourth-order integral boundary value problem with two parametersu(4)(t)+βu′′(t)-αu(t)=f(t,u),t∈(0,1),  u(0)=u(1)=0,  u′′(0)=∫01u(s)ϕ1(s)ds,u′′(1)=∫01u(s)ϕ2(s)ds, where nonlinear term functionfis allowed to change sign. Applying the fixed point index theorem on cone together with the operator spectrum theorem, some results on the existence of positive solution are obtained.

scholarly journals Multiple positive solutions of integral boundary value problem for a class of nonlinear fractional-order differential coupling system with eigenvalue argument and (p1,p2)-Laplacian

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4291-4306
Author(s):  
Kaihong Zhao
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Index Theorem ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Existence And Multiplicity ◽  
Coupling System ◽  
Differential Coupling

This paper is concerned with the integral boundary value problem for a class of nonlinear fractional order differential coupling system with eigenvalue argument and (p1,p2)-Laplacian. Some sufficient criteria have been established to guarantee the existence and multiplicity of positive solution by the fixed point index theorem in cones. Meanwhile, we obtain the range of eigenvalue parameter. As an application, one example is also provided to illustrate the validity of our main results.

scholarly journals Existence of Positive Solutions for a Fourth-Orderm-Point Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liu Yang ◽  
Chunfang Shen
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Index Theorem ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Conditions ◽  
Fixed Point Index Theorem ◽  
Krasnosel’Skii’S Fixed Point Theorem

By using Krasnosel’skii’s fixed point theorem and the fixed point index theorem in the special function space, we obtain some sufficient conditions for the existence of positive solutions of fourth-order boundary value problem with multipoint boundary conditions. Applications of our results to some special problems are also discussed.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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