We investigate the existence of positive solutions to a three-point boundary value problem of second order impulsive differential equation. Our analysis rely on the Avery-Peterson fixed point theorem in a cone. An example is given to illustrate our result.

This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem DC0+αu(t)=f(t, u(t), u'(t)), 0<t<1, u(1)=u'(1)=u''(0)=0, where 2<α≤3 is a real number, DC0+α is the Caputo fractional derivative, and f:[0,1]×[0, +∞)×R→[0, +∞) is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii's fixed point theorem and Leggett-Williams fix...

(see for example [3], [8], [9], [14], [17]–[19], [24] and the references therein). Here, λ ∈ R is a positive parameter, k is a given smooth function on R, n ≥ 3, and 2∗ = 2n/(n− 2) is the critical Sobolev exponent. Problem (0) has a geometrical relevance, since for λ = 0 every solution to (0) gives rise, up to a stereographic projection, to a metric g on the sphere whose scalar curvature is pro...

where w, p are positive and continuous on (0, 1), which allows singularities at the endpoints, and f(y) ≥ 0 and continuous for y ∈ R. For a given positive integer N , we provide conditions on the nonlinear function f which guarantee existence of N positive solutions. Our motivation comes from previous work in the case w(x) ≡ p(x) ≡ 1 of Henderson and Thompson [6], which uses a fixed point theor...

We extend ODE results of Henderson and Thompson, see [10], to a large class of boundary value problems for both ODEs and PDEs. Our method of proof combines upper and lower solutions with degree theory.

We always assume that the following hypotheses hold: (A1) p ∈ C([0,1], [0,+∞]), and ∫ 1 0 dt/p(t) < +∞; (A2) g∈ L(0,1), and g(s)≥ 0, a.e. and there exists [a,b]⊂ (0,1), such that 0< ∫ b a g(s)ds; (A3) F(t,u)∈ C([0,1]× [0,+∞],[0,+∞]). The BVP(1.1) arises in many different areas of applied mathematics and physics, and only its positive solution is significant in some practice. For the special cas...

where k1, k2 > 0 are positive constants, Ω ⊂ R is a bounded domain with a smooth boundary ∂Ω and V (u, v) ∈ C(R,R). We refer to [CdFM], [CM], [dFF], [dFM] and [HvV] for variational study of such elliptic systems. However, it seems that the multiplicity of positive solutions for such elliptic systems is not well studied. Here, we study a case related to some models (with diffusion) in mathematic...

In this paper we use the method of upper and lower solutions combined with degree theoretic techniques to prove the existence of multiple positive solutions to semipositone superlinear systems of the form −∆u = g1(x, u, v) −∆v = g2(x, u, v) on a smooth, bounded domain Ω ⊂ R with Dirichlet boundary conditions, under suitable conditions on g1 and g2. Our techniques apply generally to subcritical,...