Positive solutions to an th order right focal boundary value problem.
Positive solutions to boundary value problems of nonlinear fractional differential equations.
Positive solutions to generalized second-order three-point integral boundary-value problems.
Positive solutions to nonlinear first-order nonlocal BVPs with parameter on time scales.
Positive solutions to nonlinear higher-order nonlocal boundary value problems for fractional differential equations.
Positive solutions to nonlinear second-order three-point boundary-value problems for difference equation with change of sign.
Positive solutions to nonlinear singular second order boundary value problems
Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for...
Positive solutions to second-order singular differential equations involving the one-dimensional -Laplace operator.
Positive solutions to singular and delay higher-order differential equations on time scales.
Positive solutions to systems of nonlinear second order three-point boundary value problems.
Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities
We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.
Positive stable realizations of fractional continuous-time linear systems
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
Positive symmetric solutions of singular semipositone boundary value problems.
Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems
In this paper we consider positive unbounded solutions of second order quasilinear ordinary differential equations. Our objective is to determine the asymptotic forms of unbounded solutions. An application to exterior Dirichlet problems is also given.
Positively homogeneous functions and the Łojasiewicz gradient inequality
It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.
Positivity and stability for a system of transport equations with unbounded boundary perturbations.
Positivity and stability of the solutions of Caputo fractional linear time-invariant systems of any order with internal point delays.
Positivity conditions and bounds for Green’s functions for higher order two-point BVP
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear equations are also discussed.
Positivity of Green's matrix of nonlocal boundary value problems
We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of linear functional differential equations with the boundary conditions , , where and are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, or and can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator...
Positivity of the Green functions for higher order ordinary differential equations.