117,743 research outputs found
Existence of positive solutions for higher order three-point boundary value problems on time scales
In this paper, by using the four functionals fixed point theorem, Avery-Henderson fixed point theorem and the five functionals fixed point theorem, respectively, we investigate the conditions for the existence of at least one, two and three positive solutions to nonlinear higher order three-point boundary value problems on time scales
ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO BOUNDARY VALUE PROBLEMS ON TIME SCALES
This work formulates existence, uniqueness, and uniqueness-implies-existence theorems for solutions to two-point vector boundary value problems on time scales. The methods used include maximum principles, a priori bounds on solutions, and the nonlinear alternative of Leray-Schauder
Positive solutions for multi point impulsive boundary value problems on time scales
In this paper, we consider nonlinear second-order multi-point impulsive boundary value problems on time scales. We establish the criteria for the existence of at least one, two and three positive solutions by using the Leray-Schauder fixed point theorem, the Avery-Henderson fixed point theorem and the five functional fixed point theorem, respectively. An example that supports the theoretical results is also provided
Existence of three solutions for a first-order problem with nonlinear non-local boundary conditions
Conditions for the existence of at least three positive solutions to the
nonlinear first-order problem with a nonlinear nonlocal boundary condition
given by
&& y'(t) - p(t)y(t) = \sum_{i=1}^m f_i\big(t,y(t)\big), \quad t\in[0,1],
&& \lambda y(0) = y(1) + \sum_{j=1}^n \Phi_j(\tau_j,y(\tau_j)), \quad
\tau_j\in[0,1], are discussed, for sufficiently large . The
Leggett-Williams fixed point theorem is utilized.Comment: outline, 6 page
Variational approach to second-order impulsive dynamic equations on time scales
The aim of this paper is to employ variational techniques and critical point
theory to prove some conditions for the existence of solutions to nonlinear
impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also
we will be interested in the solutions of the impulsive nonlinear problem with
linear derivative dependence satisfying an impulsive condition.Comment: 17 page
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