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Periodic problems for ODEs via multivalued Poincaré operators

Lech Górniewicz (1998)

Archivum Mathematicum

We shall consider periodic problems for ordinary differential equations of the form x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x ( a ) , where f : [ 0 , a ] × R n → R n satisfies suitable assumptions. To study the above problem we shall follow an approach based on the topological degree theory. Roughly speaking, if on some ball of R n , the topological degree of, associated to (), multivalued Poincaré operator P turns out to be different from zero, then problem () has solutions. Next by using the multivalued version of the classical Liapunov-Krasnoselskǐ guiding potential...

Periodic solution to a multispecies predator-prey competition dynamic system with Beddington-DeAngelis functional response and time delay

Xiaojie Lin, Zengji Du, Yansen Lv (2013)

Applications of Mathematics

In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).

Periodic solutions for a class of non-autonomous Hamiltonian systems with p ( t ) -Laplacian

Zhiyong Wang, Zhengya Qian (2024)

Mathematica Bohemica

We investigate the existence of infinitely many periodic solutions for the p ( t ) -Laplacian Hamiltonian systems. By virtue of several auxiliary functions, we obtain a series of new super- p + growth and asymptotic- p + growth conditions. Using the minimax methods in critical point theory, some multiplicity theorems are established, which unify and generalize some known results in the literature. Meanwhile, we also present an example to illustrate our main results are new even in the case p ( t ) ≡ p = 2 .

Periodic solutions for differential inclusions in ℝ N

Michael E. Filippakis, Nikolaos S. Papageorgiou (2006)

Archivum Mathematicum

We consider first order periodic differential inclusions in ℝ N . The presence of a subdifferential term incorporates in our framework differential variational inequalities in ℝ N . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.

Periodic solutions for n -th order delay differential equations with damping terms

Lijun Pan (2011)

Archivum Mathematicum

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for n th order delay differential equations with damping terms x ( n ) ( t ) = ∑ i = 1 s b i [ x ( i ) ( t ) ] 2 k - 1 + f ( x ( t - τ ( t ) ) ) + p ( t ) . Some new results on the existence of periodic solutions of the investigated equation are obtained.

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