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Journals and Conferences
We study the existence of positive solutions for a class of m-point boundary value problems on time scales. Our approach is based on the monotone iterative technique and the cone expansion and compression fixed point theorem of norm type. Without the assumption of the existence of lower and upper solutions, we do not only obtain the existence of positive… (More)
In this paper, we study the existence of positive solutions to nonlinear m-point boundary-value problems for a p-Laplacian dynamic equation on time scales. We use fixed point theorems in cones and obtain criteria that generalize and improve known results.
In this article, we study a class of mixed monotone operators with perturbations. Using a monotone iterative technique and the properties of cones, we show the existence and uniqueness for fixed points for such operators. As applications, we prove the existence and uniqueness of positive solutions for nonlinear integral equations of second-order on time… (More)
In this paper, we introduce α-ψ-φ-Jachymski contractive mappings with generalized altering distance functions in the setting of quasi-metric spaces. Some theorems on the existence and uniqueness of fixed points for such mappings via admissible mappings are established. Utilizing above abstract results, we derive common fixed point theorem for two operators… (More)
In this paper, we consider a higher-order three-point boundary value problem on time scales. We study the existence of solutions of a non-eigenvalue problem and of at least one positive solution of an eigenvalue problem. Later we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also… (More)
By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales uΔ n t g t f u t , uΔ t , . . . , uΔ n−2 t 0, 0 < t < T ; uΔ i 0 0, 0 ≤ i ≤ n−3; αuΔ 0 −βuΔ ξ 0, n ≥ 3; γuΔ T δuΔ η 0, n ≥ 3, where α > 0, β ≥ 0, γ > 0, δ ≥ 0, ξ, η ∈ 0, T… (More)
In this paper, by means of τ -φ-concave (convex) operators, the existence of two positive fixed points for some nonlinear operators is considered. In particular, the fixed point theorems of the sum of a φ1-concave operator and a φ2-convex operator are obtained, our tools are based on the properties of cones and the fixed point theorem of cone expansion and… (More)
In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term. The main tools adopted in our proofs are the concentration compactness principle and Nehari manifold.
i=1 aiφ(u′′(ξi)), u(0) = 0, u(1) = m−2 ∑ i=1 biu(ξi), where φ : R −→ R is an increasing homeomorphism and homomorphism and φ(0) = 0. The nonlinear term f may change sign. As an application, an example to demonstrate our results is given. © 2008 Elsevier B.V. All rights reserved.