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# Existence and multiplicity of positive solutions for a nonlocal differential equation

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11 pages

## In this paper, the existence and multiplicity results of positive solutions for a nonlocal differential equation are mainly considered. In this paper, the existence and multiplicity results of positive solutions for a nonlocal differential equation are mainly considered.

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### biomed

Ajouté le : 01 janvier 2011
Lecture(s) : 8
Signaler un abus
##### Fixed point theorem

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Wanget al.Boundary Value Problems2011,2011:5 http://www.boundaryvalueproblems.com/content/2011/1/5
R E S E A R C HOpen Access Existence and multiplicity of positive solutions for a nonlocal differential equation 1* 2,3 3 Yunhai Wang, Fanglei Wangand Yukun An
* Correspondence: yantaicity@163. Abstract com 1 College of Aeronautics and In this paper, the existence and multiplicity results of positive solutions for a nonlocal Astronautics, Nanjing University of differential equation are mainly considered. Aeronautics and Astronautics, Nanjing 210016, Peoples Republic Keywords:Nonlocal boundary value problems, Cone, Fixed point theorem of China Full list of author information is available at the end of the article Introduction In this paper, we are concerned with the existence and multiplicity of positive solutions for the following nonlinear differential equation with nonlocal boundary value condi tion  1 q |u(s)|dϕ(s)u(t) =h(t)f(u(t)), in0<t<1 0 (1) 1   αu(0)βu(0) = 0,γu(1) +δu(1) =g u(s)dϕ(s) , 0 wherea,b,g,δare nonnegative constants,r=ag+aδ+bg> 0,q1; 1 1 q q |u(s)|dϕ(s,|u(s)|dϕ(sdenote the RiemannStieltjes integrals. Many authors consider the problem f(u) n u=M, inR,uon= 0,∂ β (2) f u because of the importance in numerous physical models: system of particles in ther modynamical equilibrium interacting via gravitational potential, 2D fully turbulent behavior of a real flow, onedimensional fluid flows with rate of strain proportional to a power of stress multiplied by a function of temperature, etc. In [1,2], the authors use the Krasnoselskii fixed point theorem to obtain one positive solution for the following nonlocal equation with zero Dirichlet boundary condition   1 q a|u(s)|u(t) =h(t)f(u(t)) 0 when the nonlinearityfis a sublinear or superlinear function in a sense to be established when necessary. Nonlocal BVPs of ordinary differential equations or system arise in a vari ety of areas of applied mathematics and physics. In recent years, more and more papers
© 2011 Wang et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.