On the nonexistence and existence of solutions for a fourth-order discrete boundary value problem.
On the nonlinear elastic simply supported beam equation.
On the nonlocal Cauchy problem for semilinear fractional order evolution equations
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first...
On the nonoscillation of second-order neutral delay differential equation with forcing term.
On the Nonoscillatory Properties of Solutions of a Functional Differential Equation
On the normal systems of differential equations
On the n-th order iterative ordinary linear differential equations.
On the number of limit cycles in perturbations of a two dimensional nonlinear differential system.
On the number of limit cycles of a generalized Abel equation
New results are proved on the maximum number of isolated -periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.
On the number of periodic solutions of a generalized pendulum equation
For a generalized pendulum equation we estimate the number of periodic solutions from below using lower and upper solutions and from above using a complex equation and Jensen’s inequality.
On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations
We study singularly perturbed 1D nonlinear Schrödinger equations (1.1). When has multiple critical points, (1.1) has a wide variety of positive solutions for small and the number of positive solutions increases to as . We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of . Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.
On the number of solutions of boundary value problems involving the -Laplacian.
On the Number of Solutions of the Equation ...= ...aj(t)xj, 0...t...1, for which x(0) = x(1).
On the number of zeros of bounded nonoscillatory solutions to higher-order nonlinear ordinary differential equations
The higher-order nonlinear ordinary differential equation is considered and the problem of counting the number of zeros of bounded nonoscillatory solutions satisfying is studied. The results can be applied to a singular eigenvalue problem.
On the number of zeros of Melnikov functions
We provide an effective uniform upper bound for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of the perturbation, and on the order of the Melnikov function. The generic case was considered by Binyamini, Novikov and Yakovenko [BNY10]. The bound follows from an effective construction of the Gauss-Manin connection for iterated integrals.
On the numerical solution of implicit two-point boundary-value problems
On the numerical solution of nonlinear partial differential equations on divergence form
On the Numerical Treatment of a Small Divisor Problem.
On the operator equation with unbounded operators , , and .
On the opial type criterion for the well-posedness of the Cauchy problem for linear systems of generalized ordinary differential equations
The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered....