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 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.

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 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 Positive Solutions for a Fourth-Order Riemann–Stieltjes Integral Boundary Value Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Yujun Cui ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Linear Operators ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Existence Of Positive Solutions

In this paper, we use the fixed point index to study the existence of positive solutions for the fourth-order Riemann–Stieltjes integral boundary value problem −x4t=ft,xt,x′t,x″t,x″′t, t∈0,1x0=x′0=x″′1=0,x″0=αx″t, where f: 0,1×ℝ+×ℝ+×ℝ+×ℝ+⟶ℝ+ is a continuous function and αx″ denotes a linear function. Two existence theorems are obtained with some appropriate inequality conditions on the nonlinearity f, which involve the spectral radius of related linear operators. These conditions allow ft,z1,z2,z3,z4 to have superlinear or sublinear growth in zi,  i=1,2,3,4.

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