Related papers: Second-order differential equation with indefinite…
An irreducible canonical approach to second-order reducible second-class constraints is given. The procedure is exemplified on gauge-fixed three-forms.
In this paper, we study the existence and multiplicity of positive solutions for a nonlinear fourth-order with multi-point boundary conditions involving an integral boundary condition. The main tool is Krasnosel'skii fixed point theorem on…
By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…
We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in…
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
In this paper, we focus our attention on the positive solutions to second-order nonlinear ordinary differential equations of the form $u''+q(t)g(u)=0$, where $q$ is a sign-changing weight and $g$ is a superlinear function. We exploit the…
In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…
We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in…
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…
Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…
We deal with the periodic boundary value problem for a second-order nonlinear ODE which includes the case of the Nagumo type equation $v_{xx} - g v + n(x) F(v) = 0,$ previously considered by Grindrod and Sleeman and by Chen and Bell in the…
We discuss the solvability of an infinite system of first order ordinary differential equations on the half line, subject to nonlocal initial conditions. The main result states that if the nonlinearities possess a suitable "sub-linear"…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…