scholarly journals Positive Solutions for a Class of Fourth-Orderp-Laplacian Boundary Value Problem Involving Integral Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yan Sun
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Integral Boundary Conditions ◽  
Index Theory ◽  
Integral Conditions ◽  
Interesting Point ◽  
Integral Boundary ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions forp-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples to demonstrate the main results.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

scholarly journals Existence, Nonexistence and Multiplicity of Positive Solutions for Singular Boundary Value Problems Involving φ-Laplacian

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 953 ◽  
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Interesting Point ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving φ -Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.

scholarly journals Existence Result for Impulsive Differential Equations with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Peipei Ning ◽  
Qian Huan ◽  
Wei Ding
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fixed Point Index ◽  
Integral Boundary Conditions ◽  
Impulsive Differential Equations ◽  
Index Theory ◽  
Upper And Lower Bounds ◽  
Point Index ◽  
Integral Boundary ◽  
Fixed Point Index Theory

We investigate the following differential equations:-(y[1](x))'+q(x)y(x)=λf(x,y(x)), with impulsive and integral boundary conditions-Δ(y[1](xi))=Ii(y(xi)),i=1,2,…,m,y(0)-ay[1](0)=∫0ωg0(s)y(s)ds,y(ω)-by[1](ω)=∫0ωg1(s)y(s)ds, wherey[1](x)=p(x)y'(x). The expression of Green's function and the existence of positive solution for the system are obtained. Upper and lower bounds for positive solutions are also given. Whenp(t),I(·),g0(s), andg1(s)take different values, the system can be simplified to some forms which has been studied in the works by Guo and LakshmiKantham (1988), Guo et al. (1995), Boucherif (2009), He et al. (2011), and Atici and Guseinov (2001). Our discussion is based on the fixed point index theory in cones.

scholarly journals Existence of positive solutions of Hadamard fractional defferential equations with integral boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-14
Author(s):  
Berhail Amel ◽  
Nora Tabouche
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Conditions ◽  
Integral Boundary ◽  
Hadamard Fractional Differential Equations ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, We study the existence of positive solutions for Hadamard fractional differential equations with integral conditions. We employ Avery-Peterson fixed point theorem and properties of Green's function to show the existence of positive solutions of our problem. Furthermore, we present an example to illustrate our main result.

Existence, multiplicity and non-existence of positive solutions for two-point boundary-value problems with strong singularity

2010 ◽  
Vol 140 (6) ◽  
pp. 1187-1196
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Image Position

We study the existence, multiplicity and non-existence of positive solutions for the singular two-point boundary-value problemswhere $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$, λ is a non-negative real parameter and f ∈ C((0, 1) × [0,∞), (0,∞)). Here, f(t, u) may be singular at t = 0 and/or 1. To obtain the main results we use the global continuation theorem and fixed-point index theory.

scholarly journals Positive solutions of singular nonlinear Sturm-Liouville boundary value problems

2004 ◽  
Vol 45 (4) ◽  
pp. 557-571
Author(s):  
Yan Sun ◽  
Lishan Liu ◽  
Yeol Je Cho
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractBy using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.

scholarly journals Solutions for a Singular Hadamard-Type Fractional Differential Equation by the Spectral Construct Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xinguang Zhang ◽  
Lixin Yu ◽  
Jiqiang Jiang ◽  
Yonghong Wu ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Operator ◽  
Nonlinear Term ◽  
Point Index ◽  
Interesting Point ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we consider the existence of positive solutions for a Hadamard-type fractional differential equation with singular nonlinearity. By using the spectral construct analysis for the corresponding linear operator and calculating the fixed point index of the nonlinear operator, the criteria of the existence of positive solutions for equation considered are established. The interesting point is that the nonlinear term possesses singularity at the time and space variables.

scholarly journals Positive Solutions for (k,n−k) Conjugate Multipoint Boundary Value Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yulin Zhao
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Real Banach Space ◽  
Boundary Value ◽  
Index Theory ◽  
Zero Element ◽  
Singular Boundary ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problems

By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem(-1)n-kun(t)=f(t,ut),0<t<1,n≥2,1≤k≤n-1,u(0)=∑i=1m-2‍aiu(ξi),u(i)(0)=u(j)(1)=θ,1≤i≤k−1,0≤j≤n−k−1in a real Banach spaceE, whereθis the zero element ofE,0<ξ1<ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2.As an application, we give two examples to demonstrate our results.

scholarly journals Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yongxiang Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Index Theory ◽  
Periodic Boundary Value Problem ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1),  i=0,1,2,3, wheref:[0,1]×R+×R→R+is continuous,α,β∈R,and satisfy0<α<((β/2)+2π2)2,β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.

scholarly journals Positive Solutions for Nonlinearq-Fractional Difference Eigenvalue Problem with Nonlocal Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Wafa Shammakh ◽  
Maryam Al-Yami
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Index Theory ◽  
Nonlocal Boundary Conditions ◽  
Fractional Difference ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The problem of positive solutions for nonlinearq-fractional difference eigenvalue problem with nonlocal boundary conditions is investigated. Based on the fixed point index theory in cones, sufficient existence of positive solutions conditions is derived for the problem.

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