相关论文: Viewing nonoscillatory second order linear differe…

Consider in a real Hilbert space $H$ the differential equation (inclusion) $(E)$: $p(t)u^{\prime \prime}(t)+q(t)u^{\prime}(t)\in Au(t)+f(t)$ for a.a. $t>0$, with the condition $(B)$: $u(0)=x \in \overline{D(A)}$, where $A\colon D(A)\subset…

This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…

We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…

\noindent Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \begin{equation*} \Delta \left(r_{n}\left(\Delta \left(x_{n}+p_{n}x_{n-k}\right) \right)…

Using the Riccati transformation techniques, we will extend some almost oscillation criteria for the second-order nonlinear neutral difference equation with quasidifferences $$\Delta\left(r_n\left(\Delta \left(x_n+c…

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…

In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential…

Earlier work introduced a method for obtaining indefinite $q$-integrals of $q$-special functions from the second-order linear $q$-difference equations that define them. In this paper, we reformulate the method in terms of $q$-Riccati…

We consider a family of solutions of $q-$difference Riccati equation, and prove the meromorphic solutions of $q-$difference Riccati equation and corresponding second order $q-$difference equation are concerning with $q-$gamma function. The…

It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when…

We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic…

This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…

The aim of this paper is to prove the existence and uniqueness of solutions of the following $q$- Cauchy problem of second order linear $q$-difference problem associated with the Rubin's $q$- difference operator $\partial_q$ in a…

We study existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci's extremal operators in dimension two. In particular we prove the existence of a positive solution of a fully…

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous…

We study the existence of global positive solutions of the differential inequalities $$ - \operatorname{div} A (x, u, \nabla u) \ge f (u) \quad \mbox{in } {\mathbb R}^n, $$ where $n \ge 2$ and $A$ is a Carath\'eodory function such that $$…

We consider Dirichlet elliptic equations driven by the sum of a $p$-Laplacian $(2<p)$ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both $\pm\infty$ and at zero. We prove an existence theorem…

In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is…

For a second-order elliptic equation of nondivergence form in the plane, we investigate conditions on the coefficients which imply that all strong solutions have first-order derivatives that are Lipschitz continuous or differentiable at a…

We study the existence of infinitely many positive homoclinic solutions to a second-order difference equation on integers with $p_k$-Laplacian. To achieve our goal we use the critical point theory and the general variational principle of…