Triple positive periodic solutions of nonlinear singular second-order boundary value problems

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.     

Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces

The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray-Schauder type and on a fixed point theorem in cones.     

Twin solutions to singular semipositone problems

In this paper, by a specially constructed cone and the fixed point index theory, we investigate the existence of multiple positive solutions for the following singular semipositone problem:

     

Singular second order boundary value problems on purely discrete time scales

We study singular discrete second order boundary value problems with mixed boundary conditions over a finite interval. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems.     

Fixed-sign solutions for a system of singular focal boundary value problems

We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution.     

Positive solutions for nonlinear singular boundary value problems

Some sufficient conditions for the existence of positive solutions to Dirichlet boundary value problems of a class of nonlinear second order differential equations are given.     

Existence and uniqueness of positive solutions for some singular boundary value problems with linear functional boundary conditions

By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f(t, u) is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0,1] positive solutions as well as the C ¹[0, 1] positive solutions.     

Symmetric positive solutions of nonlinear boundary value problems

We study the nonlinear boundary value problem

     

Multiple positive solutions for superlinear second order singular boundary value problems with derivative dependence

The existence of at least two positive solutions is presented for the singular second-order boundary value problem
{1/p（t）（ p（t）x′（t））′＋Φ（t）f（t,x（t）,p（t）x′（t））=0,0〈t〈1,
limt→0 p（t）x′（t）=0,x（1）=0
by using the fixed point index, where f may be singular at x = 0 and px ′= 0.     

Existence of positive solutions for fourth‐order impulsive integral boundary value problems on time scales

This paper is devoted to the existence of positive solutions for a fourth‐order impulsive boundary value problem with integral boundary conditions on time scales. Existence results of at least two and three positive solutions are established via the double fixed point theorem and six functionals fixed point theorem, respectively. Also, an example is given to illustrate the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Twin positive solutions of boundary value problems for finite difference equations with p-Laplacian operator

In this paper, a new twin fixed point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem

     

Positive solutions for third-order boundary value problems with change of signs

In this paper, we study the third-order triple-point nonlinear boundary value problems with sign changing nonlinearities by employing Krasnoselkii-Guo fixed point theorem and Avery-Henderson fixed point theorem,and establish results on the existence of at least one or two positive solutions to the boundary value problems.     

Existence of solutions of periodic‐type boundary value problems for multi‐term fractional differential equations

Results on the existence of solutions of a periodic‐type boundary value problem of singular multi‐term fractional differential equations with the nonlinearity depending on are established and being singular at t = 0 and t = 1. The analysis relies on the well‐known fixed‐point theorems. An example is given to illustrate the efficiency of the main theorems. Copyright © 2013 John Wiley & Sons, Ltd.     

Existence of solutions for nonlinear singular boundary value problems

Existence of solutions to the two-point boundary value problem (p(t)y')' = q(t)f(t, y,p(t)y'), y(l) = 0, lim_t→0+ p(t)y'(t) = 0 is established under a variety of conditions. Here p(0) = 0 is allowed, and q is not assumed to be continuous at 0, so the problem may be doubly singular. In addition, the Dirichlet problem for this differential equation is investigated     

四阶边值问题的非负解

讨论了一类四阶非线性常微分方程两点边值问题非负解的存在性.利用锥不动点指数理论得到了方程存在非负解的充分条件.     

An upper and lower solution approach for singular boundary value problems with sign changing non‐linearities

We obtain via Schauder's fixed point theorem new results for singular second‐order boundary value problems where our non‐linear term f(t,y,z) is allowed to change sign. In particular, our problem may be singular at y=0, t=0 and/or t=1. Copyright © 2002 John Wiley & Sons, Ltd.     

Multiple positive solutions of singular second-order m-point boundary value problems

The existence of multiple positive solutions about the singular second-order m-point boundary value problem