Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integrodifferential Equations.
Near-best approximations to the solution of Fredholm integral equation of the second kind
Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales
In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.
Necessary and sufficient well-posedness conditions for a convolution equation of the second kind with even kernel on a finite interval.
Neural networks with memory.
New conditions for the existence of non trivial solutions to some Volterra equations.
We consider the following Volterra equation:(1) u(x) = ∫0x k(x-s) g(u(s)) ds, where,k: [0, δ0] → R is an increasing absolutely continuous function such thatk(0) = 0g: [0,+ ∞) → [0,+ ∞) is an increasing absolutely continuous function such that g(0) = 0 and g(u)/u → ∞ as u → 0+ (see [3]).Let us note that (1) has always the trivial solution u = 0.Some necessary and sufficient conditions for the existence of nontrivial solutions to (1) with k(x) = xα - 1 (α>0) are given in [1], [2] and...
New convergence criteria for the Newton-Kantorovich method and some applications to nonlinear integral equations
New existence results and comparison principles for impulsive integral boundary value problem with lower and upper solutions in reversed order.
New integral inequalities for iterated integrals with applications.
New retarded integral inequalities with applications.
New spectral criteria for almost periodic solutions of evolution equations
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...
Non local solutions of a nonlinear hyperbolic partial differential equation.
Non-autonomous implicit integral equations with discontinuous right-hand side
We deal with the implicit integral equation where and where , and . We prove an existence theorem for solutions where the contituity of with respect to the second variable is not assumed.
Non-autonomous vector integral equations with discontinuous right-hand side
We deal with the integral equation , with , and . We prove an existence theorem for solutions , , where is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where does not depend explicitly on the first variable .
Noncommutative operational calculus.
Nonexistence of solutions for quasilinear elliptic equations with -growth in the gradient.
Nonlinear delay integral inequalities for piecewise continuous functions and applications.
Nonlinear equations with operators satisfying generalized Lipschitz conditions in scales.
Nonlinear functional integral equations of convolution type.
Nonlinear functional integrodifferential equations in Hilbert space.