A boundary value problem for second order fuzzy differential equations

In this paper, we interpret a two-point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept. We present a new concept of solutions and, utilizing the generalized differentiability, we investigate the problem of finding new solutions. Some examples are provided for which the new solutions are found.     

A boundary value problem for a differential equation of second order

We find the spectrum and prove a theorem on the expansion of an arbitrary function satisfying certain smoothness conditions in terms of the root functions of a boundary value problem of the type ?y″+q(x)+a/x²y=λy, y(0)=0, M(λ) y(a)+N(λ) y(b)=0, where 0   

The inverse problem for differential operators of second order with regular boundary conditions

This paper is devoted to the proof of the unique solvability of the inverse problem for second-order differential operators with arbitrary regular nonseparable boundary conditions. It is shown that the operator can be recovered from three of its spectra. As a special case, the well-known reconstruction of the Sturm-Liouville operator is accomplished.     

Existence results for -point boundary value problem of second order ordinary differential equations

This study concerns the existence of positive solutions to the boundary value problemwhere ξ_i(0,1) with 0<ξ₁<ξ₂<<ξ_n-2<1, a_i, b_i[0,∞) with and . By applying the Krasnoselskii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n-point boundary value problem.     

奇异非线性二阶微分方程Neumann边值问题

研究了一个奇异非线性二阶微分方程的Neumann边值问题,通过摄动技巧和比较原理得到了所论问题解的存在唯一性。     

Nonlinear boundary value problems for second order differential inclusions

In this paper, we study a class of nonlinear value boundary problems for second order differential inclusions with nonlinear perturbations, which satisfy the generalized Hartman condition weaker than that considered in some papers. Using techniques from multivalued analysis, theory of monotone operators and fixed points, we prove the existence of solutions in both “convex” and “nonconvex” cases. Our framework can be incorporated with Dirichlet, Neumann, and mixed boundary problems.     

A non-autonomous second order boundary value problem on the half-line

By variational arguments, the existence of a solution to a non-autonomous second-order boundary problem on the half-line is proven. The corresponding autonomous problem has no solution, revealing significant differences between the autonomous and the non-autonomous case.     

Periodic boundary value problems for second order functional differential equations

This paper deals with a periodic boundary value problem for a second order functional differential equation. We obtain the existence of extreme solutions under new concept of upper and lower solutions. Also, a mistake in a recent paper (Ding et al. in J. Math. Anal. Appl. 298:341–351, 2004) is corrected.     

Periodic and boundary value problems for second order differential equations

In this paper we study second order scalar differential equations with Sturm-Liouville and periodic boundary conditions. The vector fieldf(t,x,y) is Caratheodory and in some instances the continuity condition onx ory is replaced by a monotonicity type hypothesis. Using the method of upper and lower solutions as well as truncation and penalization techniques, we show the existence of solutions and extremal solutions in the order interval determined by the upper and lower solutions. Also we establish some properties of the solutions and of the set they form.     

Positive solution of singular Dirichlet boundary value problems for second order differential equation system

This paper investigates the existence of positive solutions of singular Dirichlet boundary value problems for second order differential system. A necessary and sufficient condition for the existence of C[0,1]×C[0,1] positive solutions as well as C¹[0,1]×C¹[0,1] positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems. Our nonlinearity fi(t,x₁,x₂) may be singular at x₁=0, x₂=0, t=0 and/or t=1, i=1,2.     

Existence of positive periodic solutions of periodic boundary value problem for second order ordinary differential equations

In this paper the existence of positive solutions are obtained for a class of second order differential equations. The proof is based on the fixed point index theory in cones.     

具超前变元的二阶微分方程三点边值问题的正解

§ 1　 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )…     

Eigenvalue for a singular second order three-point boundary value problem

In this paper, the existence of positive solutions for a singular second-order three-point boundary value problem is investigated. By using Krasnoselskii??s fixed point theorem, several sufficient conditions for the existence of positive solutions and the eigenvalue intervals on which there exist positive solutions are obtained. Finally, two examples are given to illustrate the importance of results obtained.