Limit - Point / Limit - Circle Results for Equations with Damping

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

and Applied Analysis 3 2. Main Results To simplify notations, let α 1/2 k 1 and β 2k 1 /2 k 1 . We define

Limit-point/limit-circle Results for Forced Second Order Differential Equations

In this paper, the authors consider both the forced and unforced versions of a second order nonlinear differential equation with a p-Laplacian. They give sufficient conditions as well as necessary and sufficient conditions for the unforced equation to be of the strong nonlinear limit-circle type, and they give sufficient conditions for the forced equation to be of the strong nonlinear limit-cir...

Acta Sci. Math. (Szeged)

. The spectral theory of the equation changes depending on the growth of H towards the endpoint s+; the classical distinction into the Weyl alternatives ‘limit point’ or ‘limit circle’ case. A refined measure for the growth of a limit point Hamiltonian H can be obtained by comparing with Hpolynomials. This growth measure is concretised by a number∆(H) ∈ N0∪{∞} and appeared first in connection w...

Limit Cycle Bifurcations of a Special Liénard Polynomial System

In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles surrounding a unique singular point for an arbitrary polynomial system. Then, by means of the same bifurcationally geometric approach, we solve the limit...