Note on certain nonlinear evolution equations of second order

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

Nonlinear stochastic evolution equations of second order with damping

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.

A Note on the Oscillation Theory of Certain Second Order Differential Equations

We consider the complex oscillation theory of the second order linear diierential equation f 00 + (e P(z) + Q(z))f = 0, where P(z) and Q(z) are polynomials of degrees n 1 and m 0, respectively. The situation for the case n = 1 is clear. For the case n 2, a result of Bank and Langley 4] shows that if m < 2(n ? 1), then for any non-trivial solution f of the equation, its exponent of the convergen...

Nonlinear second order evolution equations with state-dependent delays

We consider second order quasilinear parabolic equations where also the main part contains functional dependence and state-dependent delay on the unknown function. Existence and some qualitative properties of the solutions are shown.

Nonlinear Evolution Equations for Second-order Spectral Problem

Soliton equations are infinite-dimensional integrable systems described by nonlinear evolution equations. As one of the soliton equations, long wave equation takes on profound significance of theory and reality. By using the method of nonlinearization, the relation between long wave equation and second-order eigenvalue problem is generated. Based on the nonlinearized Lax pairs, Euler-Lagrange f...