In this paper, by using the classical fixed-point index theorem for compact maps and Leggett-Williams fixed point theorem, some sufficient conditions for the existence of multiple positive solutions for a class of second-order p-Laplacian boundary value problem with impulse on time scales are established. We also give an example to illustrate our results

This work investigates the existence of multiple positive solutions for a system two nonlinear higher-order fractional differential equations with ϕ-Laplacian operators and nonlocal conditions. A degenerate nonlinearity which obeys some general growth conditions is considered. The singularities are dealt by approximating fixed point operator. New results presented using index theory. Examples a...

The current paper intends to report the existence and uniqueness of positive solutions for nonlinear pantograph Caputo–Hadamard fractional differential equations. As part a procedure, we transform specified equation into an equivalent integral equation. We show that this has solution by utilising Schauder fixed point theorem (SFPT) upper lower method. Another method proving singular is Banach (...

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

This paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations. By using bifurcation and fixed point index theories in the frame of approximation arguments, the criteria of the existence, multiplicity and nonexistence of positive solutions are established. c © 2007 Elsevier Ltd. All rights reserved.

Since the fundamental theory of variational inequality was founded in the 1960s, the variational inequality theory with applications has made powerful progress and has become an important part of nonlinear analysis. It has been applied intensively to mechanics, differential equation, cybernetics, quantitative economics, optimization theory, nonlinear programming, and so forth (see [2]). In virt...

In this paper, we discuss the existence of positive periodic solutions to the nonlinear differential equation u′′(t)+ a(t)u(t) = f (t, u(t)), t ∈ R, where a : R → [0,+∞) is an ω-periodic continuous function with a(t) ≡ 0, f : R × [0,+∞) → [0,+∞) is continuous and f (·, u) : R → [0,+∞) is also an ω-periodic function for each u ∈ [0,+∞). Using the fixed point index theory in a cone, we get an ess...

Values of the parameter λ are determined for which there exist positive solutions to the third order eigenvalue problem satisfying general two-point boundary conditions. We establish the results by applying cone theory and the Krasnosel’skii fixed point theorem.