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Abstract: In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of . [Copyright &y& Elsevier]

Abstract: This paper considers the existence of positive solutions for advanced differential equations with one-dimensional p-Laplacian. To obtain the existence of at least three positive solutions we use a fixed point theorem due to Avery and Peterson. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of multiple positive solutions for the following nonlinear m-point boundary value problem (BVP)where is an increasing homeomorphism and homomorphism and with . Some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying Avery–Henderson and a new fixed-point theorems, respectively. As an application, some examples are included to illustrate the main results. In particular, our results extend and improve some known results. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the existence of multiple positive solutions for some nonlinear singular four-point boundary value problems with p-Laplacian. Under appropriate assumptions on the nonlinear terms, by applying several known fixed point theorems, sufficient conditions for the existence of at least three positive solutions are established. [Copyright &y& Elsevier]

Abstract: We study the existence of countably many positive solutions of boundary value problems on the half-line for differential equations of second-order. The fixed-point index theory and a new fixed-point theorem in cones are used. [Copyright &y& Elsevier]

Abstract: This paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problem with impulse effects. The main results here are the generalization of Jiang [Daqing Jiang, On the existence of positive solutions to second order periodic BVPs, Acta Math. Sci. 18 (1998) 31–35] for ordinary differential equations. Existence is established via the theory of fixed point index in cones. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a discrete second-order quasi-linear boundary value problem which nonlinear term f is involved with the first order difference. By using a generalization of the Leggett–Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the multipoint boundary value problem for one-dimensional p-Laplaciansubject to the boundary value conditions:where ϕ p (s)=∣s∣ p−2 s, p >1, with and satisfy . The nonlinear term f may change sign. Using a fixed point theorem for operators in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. [Copyright &y& Elsevier]

Abstract: In this paper we present some new existence results for singular semipositone Dirichlet boundary value problem for second-order impulsive differential equations using the upper and lower solutions method and a fixed point theorem in cones. [Copyright &y& Elsevier]

Abstract: Using two numerical methods, we will show the existence of multiple solutions for the well-known logistic equation for , with Dirichlet boundary condition. [Copyright &y& Elsevier]

Abstract: Using numerical methods, we will show the existence of multiple solutions for the well known logistic equation −Δu = λ g(x)u(1− u) for x ∈ Ω, with Dirichlet boundary condition. [Copyright &y& Elsevier]

Abstract: Using numerical methods, we will show the existence of multiple solutions for the equation −Δu = λf(u) with Dirichlet boundary condition in a bounded domain Ω, where λ >0 and f(u) is a superlinear function of u. [Copyright &y& Elsevier]

New results on the existence of multiple positive solutions of a Hammerstein integral equation of the formare obtained, where f may have singularities in its first or second variable. These results generalize some previous results obtained by the author. Applications of these results are given to the existence of multiple positive solutions for singular first or second order differential equations with periodic boundary conditions. These results are often new and some of them improve many known results. [Copyright &y& Elsevier]

In this paper, the author obtains the existence of two positive solutions for a boundary value problem of nth order nonlinear integro-differential equations on an infinite interval in a Banach space by means of fixed point index theory. [Copyright &y& Elsevier]

We consider the following boundary value problem: (ϕp(y′))′+q(t)f(y)=0, p>1, t∈[0,1], with y(0)=y(1)=0, or y(0)=y′(1)=0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. An example is also included to illustrate the importance of the result obtained. [Copyright &y& Elsevier]