Generalized Riccati Inequality Research Articles

Hille-Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale

This article deals with half-linear dynamic equations that have two types of derivatives, and obtains sufficient conditions for all solutions to be non-oscillatory. The obtained results extend a previous Hille-Nehari type theorems for problems of dynamic equations. To prove our main result, we use a generalized Riccati inequality. As an application, we apply the main result to self-adjoint Euler type linear differential and difference equations with a changing sign coefficient. The equation selected for this application is of Mathieu type. For more information see https://ejde.math.txstate.edu/Volumes/2021/78/abstr.html

Nonoscillation and exponential stability of the second order delay differential equation with damping

AbstractFor a delay differential equationx¨(t)+a(t)x˙(t)+∑k=1mbk(t)x(gk(t))=0,gk(t)≤t,$$\ddot{x}(t) + a(t)\dot{x}(t)+ \displaystyle\sum\limits_{k=1}^m b_k(t)x(g_k(t))=0, g_k(t)\leq t, $$a generalized Riccati inequality is constructed for nonoscillation and exponential stability of the differential equation.

Some oscillation theorems for a class of quasilinear elliptic equations

Oscillation criteria are obtained for quasilinear elliptic equations of the form (E)below. We are mainly interested in the case where the coefficient function oscillates near infinity. Generalized Riccati inequalities are employed to establish our results.

Some Oscillation Problems for a Second Order Linear Delay Differential Equation

For the delay differential equation[formula]a connection between the following properties is established: non-oscillation of the differential equation and the corresponding differential inequality, positiveness of the fundamental function, and the existence of a nonnegative solution of a generalized Riccati inequality. Explicit conditions for non-oscillation and oscillation and comparison theorems are presented.