Related papers: Existence theorems for a nonlinear second-order di…

In this article, using DiPerna-Lions theory \cite{Di-Li}, we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and…

We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…

We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving operators corresponding to regular (nonsymmetric) Dirichlet…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…

We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…

We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…

We derive a priori estimates for second order derivatives of solutions to a wide calss of fully nonlinear elliptic equations on Riemannian manifolds. The equations we consider naturally appear in geometric problems and other applications…

The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…

In this paper we derive a sufficient condition for the existence of a unique solution of a Cauchy type q-fractional problem (involving the fractional q-derivative of Riemann-Liouville type) for some nonlinear differential equations. The key…

Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…

In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the…

In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…

We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\"odinger type and have recently been obtained in \cite{DLS}…

This article contains a new discussion for the generalized fractional Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We study an existence and continuation of its solution. Firstly, we establish a new theorems…

To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is…

We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…

Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…