The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem

Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.

TWO POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR BOUNDARY VALUE PROBLEMS

An existence theorem of two positive solutions of the singular BVPwas established by using topological degree theory.

Existence of Positive Solutions for Singular Second-order m-Point Boundary Value Problems

The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ i ∈ (0, 1) with 0 【 ξ1 【 ξ2 【 · · · 【 ξ m−2 【 1, a i ∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions.

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS OF SECOND ORDER NONLINEAR EQUATION

In this paper, we establish the existence of positive solutions of (|y'| p-2g' )'+f(t,y)= 0 (P>1 ). y (0)=y (1) = 0. The function f is allowed to be singular when y= 0.

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS

New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.

POSITIVE SOLUTIONS OF NONLINEAR FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

By constructing a special cone and using the fixed point theorem of cone expansion and compression, this paper investigates fourth-order singular boundary value problems with sublinear effect and presents some necessary and sufficient conditions for existence of C2 or C3 positive solutions. Further, some examples are given concerning the applications of our main results.

MULTIPLE POSITIVE SOLUTIONS OF A CLASS OF THREE-POINT SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper, the existence theorem for three positive solutions is presented for the singular nonlinear boundary value problem by applying the extended Five Functionals fixed point theorem.

MULTIPLE POSITIVE SOLUTIONS OF NONRESONANT SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

This paper studies the existence of multiple positive solutions of nonresonant singular boundary value problem of second order ordinary differential equations. A sufficient condition for the existence of C[0,1] multiple positive solutions as well as C1[0, 1] multiple positive solutions is given by means of the fixed point theorems on cones.

Positive Solutions of Singular Boundary Value Problems of Fourth-Order Differential Equations

The singular boundary value problem (4)(x) h(x)f((x)) = 0, 0 < x < 1, (0) = (1) = (0) = (1) = 0 is considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where h(x) is allowed to be singular at both x = 0 and x = 1. The existence results of positive solutions are obtained by means of the cone theory and the fixed point index.

EXISTENCE RESULTS FOR SEMIPOSITONE BOUNDARY VALUE PROBLEMS

The authors study the existence of positive solutions to the boundary value problem where f and e: [r,R] x [0,∞) → R are two continuous functions satisfying f 0 and |e| M for some M > 0. The authors show that there exists at least one positive solution in the following two cases: (i) f is superlinear at infinity and λ > 0 is small enough; (ii) f is sublinear at infinity and λ > 0 is large enough. Their proofs are based on fixed point theorems in cones.

Positive Solution for a Singular Fourth-Order Differential System

In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system u(4) = φu + f (t, u, u”, φ), 0 < t < 1, -φ” = μg (t, u, u”), 0 < t < 1, u (0) = u (1) = u”(0) = u”(1) = 0, φ (0) = φ (1) = 0;where μ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.

Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

This paper is devoted to the study ofthe existence of single and multiple positive solutions for the first order boundary value problem x′= f（t, x）, x（0） = x（T）, where f ∈ C（[0,T] × R） . In addition, we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin. Our proofs are based on a fixed point theorem in cones. Our results improve some recent results in the literatures.

Singular Nonlinear Boundary Value Problems Arising in the Boundary Layer Behind Expansion Wave

A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching tech- nique.And a theoretical estimate formula for skin friction coefficient is presented.The numerical solution is presented by using the shoot method.The reliability and efficiency of the theoretical prediction are verified by numerical results.

ON A SINGULAR QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM

In this paper, we establish a sufficient condition for the existence of positive solutions of problem where 0 <α, 0 < q, 0 < λ, 1 < p and , is a bounded domain with C1,γ boundary for some γ∈ (0, 1).

一类Positone边值问题正解的存在性

对一类具有奇性Positone边界值问题进行了研究,利用非线性二择一不动点定理建立了问题正解的3个存在性原则.

一类Positone边值问题正解的存在性

对一类具有奇性的Positone边值问题{(φp(y′))′+μq(t)f(t,y)=00<t<1y(0)=a≥0y(1)=b≥a进行了研究,其中:μ是一个非负常数,φp(y)=|y|p-2y,p≥2为P-Lapacian算子.利用Leray-Schauder非线性原理建立了该问题正解存在的2个判别准则.

A SECOND-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SINGULAR AND DISCONTINUOUS NONLINEARITY

In this paper, we study a nonlinear second-order periodic boundary value problem, in which the equation has a singular and discontinuous nonlinearity. By using perturbation techniques and comparison principles, we obtain the existence of solutions for this problem.

变系数三阶周期边值问题的正解(英文)

研究了变系数非线性三阶周期边值问题的正解.非线性项可以关于空间变元奇异.利用适当的变换此问题被转换为一个Hammerstein积分方程,利用锥上的Guo-Krasno-selski不动点定理获得了1～2个正解的存在性.

非线性三阶三点边值问题的正解

通过运用不动点指数理论对于一类非线性三阶常微分方程三点边值问题建立其至少存在两个正解的若干存在性准则.

二阶奇异非线性微分方程边值问题的正解

分别在0≤f+0 <M1,m1<f- ∞ ≤∞和 0 ≤f+∞ <M1,m1<f- 0 ≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u) =0 ,0 <t <1,αu( 0 ) - βu′( 0 ) =0 ,γu( 1) +δu′( 1) =0 正解的存在性 ,其中f +0 =limu→ 0 f(u) /u ,f- ∞ =limu→∞f(u) /u ,f- 0 =limu→ 0 f(u) /u ,f +∞=limu→∞f(u) /u ,g在区间 [0 。