Positive solutions for semi-positone three-point boundary value problems

Using a fixed point theorem of generalized cone expansion and compression we present in this paper criteria which guarantee the existence of at least two positive solutions for semi-positone three-point boundary value problems with parameter λ>0$\lambda >0$ belonging to a certain interval.     

The existence of countably many positive solutions for singular multipoint boundary value problems

In this paper, we study the existence of countably many positive solutions for a singular multipoint boundary value problem. By using fixed-point index theory and the Leggett-Williams’ fixed-point theorem, sufficient conditions for the existence of countably many positive solutions are established.     

Existence of multiple positive solutions of singular nonlinear boundary value problems

For a given positive integer N, we provide conditions on the nonlinear function f which guarantee that the boundary value problem

     

Triple positive solutions for boundary value problems on infinite intervals

This paper deals with the existence of triple positive solutions for Sturm–Liouville boundary value problems of second-order nonlinear differential equation on a half line. By using a fixed point theorem in a cone due to Avery–Peterson, we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term.     

On Sturm–Liouville boundary value problems for second-order nonlinear functional finite difference equations

Motivated by the interesting paper [I. Karaca, Discrete third-order three-point boundary value problem, J. Comput. Appl. Math. 205 (2007) 458–468], this paper is concerned with a class of boundary value problems for second-order functional difference equations. Sufficient conditions for the existence of at least one solution of a Sturm–Liouville boundary value problem for second-order nonlinear functional difference equations are established. We allow f to be at most linear, superlinear or sublinear in obtained results.     

Multiple positive solutions of singularly perturbed differential systems with different orders

In this paper, we consider the multiplicity of positive solutions for a class of singular higher-order perturbed differential systems with different orders. By employing a well-known fixed point theorem, some new existence results are given under the case where nonlinearity can be sign changing.     

Multiplicity of sign-changing solutions for some four-point boundary value problem

In this paper we obtain using Leray–Schauder degree theory some multiplicity results for sign-changing solutions of a four-point boundary value problem. We assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f$f$.     

Multipoint boundary value problems for nonlinear ordinary differential equations

In this paper we provide sufficient conditions for the existence of solutions to multipoint boundary value problems for nonlinear ordinary differential equations. We consider the case where the solution space of the associated linear homogeneous boundary value problem is less than 2. When this solution space is trivial, we establish existence results via the Schauder Fixed Point Theorem. In the resonance case, we use a projection scheme to provide criteria for the solvability of our nonlinear boundary value problem. We accomplish this by analyzing a link between the behavior of the nonlinearity and the solution set of the associated linear homogeneous boundary value problem.     

Solvability of second-order nonlinear three-point boundary value problems

We are interested in the existence of nontrivial solutions to the three-point boundary value problem (BVP):

(∗)     

Existence of Positive Solutions for Operator Equations and Applications to Semipositone Problems

In this paper we study the existence of positive solutions of the following operator equation in a Banach space E: where G(x, λ) = λKFx+e₀, K: E↦ E is a linear completely continuous operator, F: P↦ E is a nonlinear continuous , bounded operator, e₀∈ E, λ is a parameter and P is a cone of Banach space E. Since F is not assumed to be positive and e₀ may be a negative element, the operator equation is a so-called semipositone problem. We prove that under certain super-linear conditions on the operator F the operator equation has at least one positive solution for λ > 0 sufficiently small, and that under certain sub-linear conditions on the operator F the operator equation has at least one positive solution for λ > 0 sufficiently large. In addition, we briefly outline an application of our results which simplify previous theorems in the literature.     

The existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method

In this paper, we study the existence and multiplicity of classical solutions for a second-order impulsive differential equation with periodic boundary conditions. By using a variational method and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter pair (c,λ) lies in different intervals, respectively. Some examples are given in this paper to illustrate the main results.     

Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions

The nonlinear nth-order singular nonlocal boundary value problem

     

On the existence of positive solution for a kind of multi-point boundary value problem at resonance

This paper concerns the existence of positive solution for a class of second-order m-point boundary value problems under different resonant conditions. By using the Leggett-Williams norm-type theorem due to O’Regan and Zima, we obtain the existence of positive solution. An example is given to demonstrate the main results.     

Boundary value problems for first order functional differential equations with impulsive integral conditions

In this paper, by using the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for existence of extreme solutions for first order functional differential equations with a new impulsive integral condition. Some comparison results are also formulated.