A multiplicity result for periodic solutions of Liénard equations with an attractive singularity

A graph-theoretic method to study the existence of periodic solutions for a coupled Rayleigh system via inequality techniques

“…Up to now, the global existence of periodic solutions for differential systems has been investigated mainly by employing the following five methods: (1) Fixed point theorem methods [26]; (2) Combining continuation theorem of coincidence degree theory with the a priori estimate of periodic solutions [9,11,[13][14][15][27][28][29][30]; (3) Combining continuation theorem of coincidence degree theory with LMI [12]; (4) Combining continuation theorem of coincidence degree theory with Lyapunov function method [16,[18][19][20][21]31]; (5) The method of upper and lower functions. But, in the above-mentioned methods, (3) and (4) are used in recent years to study the existence of periodic solutions for different systems.…”

Existence and multiplicity of periodic solutions to differential equations with attractive singularities

“…The idea how to obtain multiplicity results is similar to the previous works, usually we use homotopy invariance and additivity property of Leray-Schauder degree (see, e.g. [2,6,7,15,19,23,30]). However, the nature of this kind of problems request quite new approach in how to construct the strict lower and upper functions.…”

Positive periodic solution for indefinite singular Liénard equation with p-Laplacian

“…For more works about superlinear/sublinear problems with a weight function having an indefinite sign, see e.g. [21][22][23][24][25][26].…”