共查询到20条相似文献,搜索用时 15 毫秒
1.
Qing Liu Yao 《数学学报(英文版)》2014,30(2):361-370
This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″(t) + λ(t)u(t) = f(t,u(t)),a.e.t ∈ [0,2π],u(0) = u(2π),u′(0) = u′(2π),where f(t,u) is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett–Williams and Krasnosel'skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations. 相似文献
2.
In this paper,we study the existence of positive solutions for the nonlinear singular third-order three-point boundary value problemu (t) = λa(t)f(t,u(t)),u(0) = u (1) = u (η) = 0,where λ is a positive parameter and 0 ≤ η 1 2 .By using the classical Krasnosel’skii’s fixed point theorem in cone,we obtain various new results on the existence of positive solution,and the solution is strictly increasing.Finally we give an example. 相似文献
3.
In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained. 相似文献
4.
Limei Song 《Annals of Differential Equations》2012,(3):320-326
In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results. 相似文献
5.
In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η∈ (0, 1), α∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ∈ (0, λ*) under certain conditions on the nonlinear term f. 相似文献
6.
《数学物理学报(B辑英文版)》2017,(5)
We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ(u′))′= λf(u), x ∈(0, 1),u′(0) = 0 = u′(1),where λ is a positive parameter, φ(s) =s/(1-s~2)~(1/2), f ∈ C~1([0, ∞), R), f′(u) 0 for u 0, and for some 0 β θ such that f(u) 0 for u ∈ [0, β)(semipositone) and f(u) 0 for u β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C~2([0, β) ∪(β, ∞), R),f′′(u) ≥ 0 for u ∈ [0, β) and f′′(u) ≤ 0 for u ∈(β, ∞), then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results. 相似文献
7.
This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term. 相似文献
8.
Wang Weibing Luo Zhiguo 《Annals of Differential Equations》2007,23(1):72-77
The existence of the positive solutions of a certain second order singular differential equation is studied. Our result is based on fixed-point theorem of cone expansion and compression. 相似文献
9.
EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL
By the fixed point theorem on a cone and monotone iterative technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f(t,u) increases in u. 相似文献
10.
The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″(t)=f(t,u(t)),a.e,t∈[0,1],u(0)=u′(η)=u″(1)=0, where the nonlinear term f(t, u) is a Caratheodory function and there exists a nonnegative function h ∈ L^1[0, 1] such that f(t, u) 〉 ≥-h(t). The existence of n positive solutions is proved by considering the integrations of "height functions" and applying the Krasnosel'skii fixed point theorem on cone. 相似文献
11.
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u (t) + λf (t, u) = 0, t ∈ (0, 1), u (0) = sum (biu (ξ i )) from i=1 to m-2, u(1)= sum (aiu(ξ i )) from i=1 to m-2, where λ > 0 is a parameter, 0 < ξ 1 < ξ 2 < ··· < ξ m 2 < 1 with 0 相似文献
12.
Yao Qingliu 《Annals of Differential Equations》2006,22(1):87-94
By using Krasnosel'skii fixed point theorem of cone expansion-compression type, the results on the existence of one, two and three positive solutions are established for a semilinear second-order system of two-point boundary value problems. 相似文献
13.
In this paper, we investigate the existence and uniqueness of solutions for a new fourth-order differential equation boundary value problem:{u(4)(t) = f(t, u(t))-b, 0 t 1,u(0) = u′(0) = u′(1) = u(3)(1) = 0,where f ∈ C([0,1] ×(-∞,+∞),(-∞, +∞)),b ≥ 0 is a constant. The novelty of this paper is that the boundary value problem is a new type and the method is a new fixed point theorem ofφ-(h,e)-concave operators. 相似文献
14.
Nodal solutions for a nonlinear fourth-order eigenvalue problem 总被引:2,自引:0,他引:2
Ru Yun MA Bevan THOMPSON 《数学学报(英文版)》2008,24(1):27-34
We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa(x)f(y),0〈x〈1,y(0)=y(1)=y″(0)=y″(1)=0where λ is a positive parameter, a ∈ C([0, 1], (0, ∞), f ∈C(R,R) satisfies f(u)u 〉 0 for all u ≠ 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques. 相似文献
15.
In this paper,we are interested in the existence of positive solutions for the Kirchhoff type problems{-(a_1 + b_1M_1(∫_?|▽u|~pdx))△_(_pu) = λf(u,v),in ?,-(a_2 + b_2M_2(∫?|▽v|~qdx))△_(_qv) = λg(u,v),in ?,u = v = 0,on ??,where 1 p,q N,M i:R_0~+→ R~+(i = 1,2) are continuous and increasing functions.λ is a parameter,f,g ∈ C~1((0,∞) ×(0,∞)) × C([0,∞) × [0,∞)) are monotone functions such that f_s,f_t,g_s,g_t ≥ 0,and f(0,0) 0,g(0,0) 0(semipositone).Our proof is based on the sub-and super-solutions techniques. 相似文献
16.
Hongping Wu 《Annals of Differential Equations》2011,(3):379-383
In this paper,we study a singular third-order three-point boundary value problem. By a fixed point theorem of cone expansion-compression type due to Krasnosel'skii,we obtain various new results on the existence of two positive solutions to the problem,whose coefficient is allowed to have suitable singularities. Finally,we give an example to verify our results. 相似文献
17.
《数学季刊》2015,(1)
In this paper, we consider the three-point boundary value problem(op(u′′(t)))′+a(t)f(t, u(t), u′(t), u′′(t)) = 0, t ∈ [0, 1] subject to the boundary conditions u(0) =βu′(0), u′(1) = αu′(η), u′′(0) = 0, where op(s) = |s|p-2s with p 1, 0 α, η 1and 0 ≤ β 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. 相似文献
18.
Bai Dingyong Xu Yuantong 《Annals of Differential Equations》2005,21(3):237-242
The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones. 相似文献
19.
We consider the second-order differential equation u(t) + q(t)f(t,u(t),u (t)) = 0,0 t 1,subject to three-point boundry condition u(0) = 0,u(1) = a 0 u(ξ 0 ),or to m-point boundary conditionu (0) = m2 i=1 b i u (ξ i ),u(1) = m2 i=1 a i u(ξ i ).We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson. 相似文献
20.
In this paper,we consider the following quasilinear diferential equation(p(u′))′+λf(t,u)=0subject to one of the two boundary conditions:u(0)=u′(1)=0,u′(0)=u(1)=0.After transforming them into a problem of symmetrical solutions,the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri.An example is given to demonstrate our main result. 相似文献