Existence of positive solutions for a system of semipositone coupled discrete boundary value problems

We study the existence of positive solutions for a system of nonlinear second-order difference equations with parameters and sign-changing nonlinearities, subject to multi-point coupled boundary conditions. In the proof of our main theorems we use the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.     

Existence of positive solutions of higher-order quasilinear ordinary differential equations

In this paper the even-order quasilinear ordinary differential equation is considered under the hypotheses that n is even, D(α _i )x = (|x|αi−1 x)′, α _i > 0(i = 1,2,…, n), β > 0, and p(t) is a continuous, nonnegative, and eventually nontrivial function on an infinite interval [a, ∞), a > 0. The existence of positive solutions of (1.1) is discussed, and basic results to the classical equation are extended to the more general equation (1.1). In particular, necessary and sufficient integral conditions for the existence of positive solutions of (1.1) are established in the case α ₁α₂⋅s α _n ≠ β. This research was partially supported by Grant-in-Aid for Scientific Research (No. 15340048), Japan Society for the Promotion of Science. Mathematics Subject Classification (2000) 34C10, 34C11     

Existence of positive solutions for fractional boundary value problems

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some $p > 1$, we discuss the existence and multiplicity of positive solutions to the four point boundary value problems of nonlinear fractional differential equations. Our results extend some recent works in the literature.     

Existence of multiple positive solutions for fourth order two-point boundary value problems

The present article tackles two-point boundary value problems for fourth-order differential equations as follows <artwork name="GAPA31044eu1"> Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results.     

Existence of multiple positive periodic solutions for functional differential equations

In our paper, by employing Krasnoselskii fixed point theorem, we investigate the existence of multiple positive periodic solutions for functional differential equations

     

一类四阶两点边值问题正解的存在性

运用上下解方法及拓扑度理论讨论了非齐次边界条件下四阶两点边值问题u″″(t)=f(u(t)),t∈(0,1),u(0)=u″(0)=u″(1)=0,u(1)=λ,其中λ＞0为参数,f∈C([0,+∞),[0,+∞)).在非线性项满足一定的增长条件下,获得了上述问题存在正解时λ的取值范围.     

Existence and multiplicity for positive solutions of a second-order multi-point discrete boundary value problem

We investigate the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations with multi-point boundary conditions.     

Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control

Sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback control

The method involves the application of Krasnoselskii's fixed point theorem and estimates of uniform upper and lower bounds of solutions. When these results are applied to some special delay population models with multiple delays, some new results are obtained and some known results are generalized.     

Three positive solutions of nonhomogeneous semilinear elliptic equations

In this paper, we use new analyses to assert that there are three positive solutions of Eq. (1.1) in infinite cylinder domain with hole .     

Nonexistence and existence of positive solutions for the Kirchhoff type equation

In this paper, we study the nonexistence and existence of positive solutions for the Kirchhoff type equation with nonlinearity having prescribed asymptotic behavior. Because of the structure of our equation, our nonexistence results have some special properties, and our conditions for positive solutions are also different from the existing results.     

Existence of multiple positive solutions for inhomogeneous Neumann problem

In this paper, we study the existence and nonexistence of multiple positive solutions for the inhomogeneous Neumann boundary value problem

(∗)     

Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions

We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions.     

Existence of positive solutions for second-order boundary value problem with one parameter

In the case of not requiring f(t,u) to be nonnegative, by transforming the boundary value problem into the integral equation system, and applying the fixed point index theory, the author studies the following second-order boundary value problem with one parameter

     

The uniqueness of solutions to discrete, vector, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.     

The effect of domain shape on the number of positive and nodal solutions for semilinear elliptic equations

In this paper, we study the effect of domain shape on the number of positive and nodal (sign-changing) solutions for a class of semilinear elliptic equations. We prove a semilinear elliptic equation in a domain Ω$\Omega$ that contains m$m$ disjoint large enough balls has m²$m^2$ 2-nodal solutions and m$m$ positive solutions.     

Existence of positive bounded solutions for some nonlinear elliptic systems

We prove some existence results of positive bounded continuous solutions to the semilinear elliptic system Δu=λp(x)g(v), Δv=μq(x)f(u) in domains D with compact boundary subject to some Dirichlet conditions, where λ and μ are nonnegative parameters. The functions f,g are nonnegative continuous monotone on (0,∞) and the potentials p, q are nonnegative and satisfy some hypotheses related to the Kato class K(D).