scholarly journals Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Stieltjes Integral ◽  
Integral Conditions ◽  
Existence Of Positive Solutions

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term:−u′′(t)=λ[f(t,u(t))−q(t)],0<t<1,αu(0)−βu′(0)=∫01u(s)dξ(s),γu(1)+δu′(1)=∫01u(s)dη(s),whereλ>0is a parameter;f:(0,1)×(0,∞)→[0,∞)is continuous;f(t,x)may be singular att=0,t=1,andx=0, and the perturbed termq:(0,1)→[0,+∞)is Lebesgue integrable and may have finitely many singularities in(0,1), which implies that the nonlinear term may change sign.

scholarly journals Exact Multiplicity of Solutions for a Class of Singular Generalized One-Dimensionalp-Laplacian Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Youwei Zhang
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Point Theory ◽  
One Dimensional ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Exact Multiplicity Of Solutions ◽  
Exact Multiplicity

We describe the existence of positive solutions for a class of singular generalized one-dimensionalp-Laplacian problem. By applying the related fixed point theory in cone, some new and general results on the existence of positive solutions to the singular generalizedp-Laplacian problem are obtained. Note that the nonlinear termfinvolves the first-order derivative explicitly.

scholarly journals Analysis on Existence of Positive Solutions for a Class Second Order Semipositone Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yunhai Wang ◽  
Xu Yang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solution ◽  
Positive Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Existence Of Positive Solutions ◽  
Bounded Below

In this paper, we study the existence of positive solutions of the following second-order semipositone system (see equation 1). By applying a well-known fixed-point theorem, we prove that the problem admits at least one positive solution, if f is bounded below.

scholarly journals Positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence

2015 ◽  
Vol 23 (2) ◽  
pp. 279-304 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Point Theory ◽  
Multiple Positive Solutions ◽  
Integral Conditions ◽  
Nonlocal Boundary Value Problems

Abstract In this paper using a fixed point theory on a cone we present some new results on the existence of multiple positive solutions for singular nonlocal boundary value problems involving integral conditions with derivative dependence.

scholarly journals FIXED POINTS AND STABILITY OF A CLASS OF NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS

2017 ◽  
pp. 031
Author(s):  
Hocine Gabsi ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Zero Solution ◽  
Point Theory ◽  
Second Order ◽  
Asymptotically Stable ◽  
Variable Delays ◽  
Nonlinear Delay

In this work we study a class of second order nonlinear neutral integro-differential equations    x(t)+f(t,x(t),x(t))x(t)+∑_{j=1}^{N}∫_{t-τ_{j}(t)}^{t}a_{j}(t,s)g_{j}(s,x(s))ds    +∑_{j=1}^{N}b_{j}(t)x′(t-τ_{j}(t))=0,with variable delays and give some new conditions ensuring that the zero solution is asymptotically stable by means of the fixed point theory. Our work extends and improves previous results in the literature such as, D. Pi <cite>pi2,pi3</cite> and T. A. Burton <cite>b12</cite>. An example is given to illustrate our claim.

scholarly journals Existence of Positive Solution for Semipositone Fractional Differential Equations Involving Riemann-Stieltjes Integral Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei Wang ◽  
Li Huang
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Stieltjes Integral ◽  
Integral Conditions ◽  
Technical Approach ◽  
Integral Boundary ◽  
Fractional Differential

The existence of at least one positive solution is established for a class of semipositone fractional differential equations with Riemann-Stieltjes integral boundary condition. The technical approach is mainly based on the fixed-point theory in a cone.

scholarly journals Positive Solutions forp-Laplacian Fourth-Order Differential System with Integral Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Value System ◽  
Existence Of Positive Solutions

This paper investigates the existence of positive solutions for a class of singularp-Laplacian fourth-order differential equations with integral boundary conditions. By using the fixed point theory in cones, explicit range forλandμis derived such that for anyλandμlie in their respective interval, the existence of at least one positive solution to the boundary value system is guaranteed.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

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