New existence results for nonlinear fractional differential equations with three-point integral boundary conditions.
New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations
This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is...
New existence results on nonhomogeneous Sturm-Liouville type BVPs for higher-order p-Laplacian differential equations
A class of nonlinear boundary value problems for p-Laplacian differential equations is studied. Sufficient conditions for the existence of solutions are established. The nonlinearities are allowed to be superlinear. We do not apply the Green's functions of the relevant problem and the methods of obtaining a priori bounds for solutions are different from known ones. Examples that cannot be covered by known results are given to illustrate our theorems.
New existence theorems of positive solutions for singular boundary value problems.
New fixed point theorems of mixed monotone operators and applications to singular boundary value problems on time scales.
New functional spaces and linear nonstationary problems of mathematical physics
New interval oscillation criteria for second-order functional differential equations with nonlinear damping
This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate...
New method for computation of discrete spectrum of radical Schrödinger operator
A new method for computation of eigenvalues of the radial Schrödinger operator is presented. The potential is assumed to behave as if and as if . The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function . It is shown that the eigenvalues are the discontinuity points of the function . Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...
New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
The nonimprovable sufficient conditions for the unique solvability of the problem where is a linear bounded operator, , , are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator is not of Volterra’s type with respect to the point .
New oscillation criteria for first order nonlinear delay differential equations
New oscillation criteria are obtained for all solutions of a class of first order nonlinear delay differential equations. Our results extend and improve the results recently obtained by Li and Kuang [7]. Some examples are given to demonstrate the advantage of our results over those in [7].
New oscillation criteria for second-order delay differential equations with mixed nonlinearities.
New oscillation criteria for second-order neutral delay differential equations with positive and negative coefficients.
New polynomials for which has a solution with almost all real zeros.
New qualitative methods for stability of delay systems
A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known...
New result in the ultimate boundedness of solutions of a third-order nonlinear ordinary differential equation.
New result of existence of periodic solution for a Hopfield neural networks with neutral time-varying delays.
New result on the ultimate boundedness of solutions of certain third-order vector differential equations
Sufficient conditions are established for ultimate boundedness of solutions of certain nonlinear vector differential equations of third-order. Our result improves on Tunc’s [C. Tunc, On the stability and boundedness of solutions of nonlinear vector differential equations of third order].
New results of a class of two-neuron networks with time-varying delays.
New results on asymptotic behavior of solutions of certain third-order nonlinear differential equations
New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model
This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays, which is defined on the nonnegative function space. Under appropriate conditions, we establish some criteria to ensure that all solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give an example with numerical simulations to illustrate our main results.