Related papers: General solution of a second order non-homogenous …
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…
In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the…
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…
Bagderina \cite{Bagderina2013} solved the equivalence problem for a family of scalar second-order ordinary differential equations (ODEs), with cubic nonlinearity in the first-order derivative, via point transformations. However, the…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.
We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with H\"older continuous coefficients. The result we obtain is essentially based on parametrix method.
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems,…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are…
We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one studied in [9], in that in this paper we consider some cases of operators with complex…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and…
We have discussed the problem of finding the condition on coefficients of $f''+A(z)f'+B(z)f=0, \quad B(z)(\not \equiv 0)$ so that all non-trivial solutions are of infinite order. The hyper-order of these non-trivial solutions of infinite…
The objective of this paper is to complete certain issues from our recent contribution [J. Calatayud, J.-C. Cort\'es, M. Jornet, L. Villafuerte, Random non-autonomous second order linear differential equations: mean square analytic…