A third order operator with periodic coefficients on the real line

THIRD ORDER LINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS i

The third order linear differential equation Ly = y'" + p2(t)y" + P\{i)y' + Po(')y = 0 is studied, where />,(/) are continuous real-valued and periodic of period 0. Various criteria are obtained which guarantee "partial" asymptotic stability or instability by means of effective bounds on the Floquet characteristic multipliers of Ly = 0.

Almost periodic solutions for some higher-order nonautonomous differential equations with operator coefficients

Keywords: Schauder fixed point principle Exponentially stable Acquistapace–Terreni conditions Evolution families Almost periodic Higher-order differential equation with operator coefficients Wave equation with fractional damping a b s t r a c t In this paper, we make extensive use of the well-known Schauder fixed point principle and the exponential stability of the evolution family involved to ...

Periodic Solutions for Third-order Nonlinear Delay Differential Equations with Variable Coefficients

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + d dt g (t, x (t− τ (t))) , is considered. By employing Green’s function, Krasnoselskii’s fixed point theorem and the contraction mapping principle, we state and prove the existence and uniqueness of periodic solutions...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Initial coefficients of starlike functions with real coefficients

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions