Periodic solutions of Volterra integral equations

Nontrivial Periodic Solutions of Some Volterra Integral Equations

I. Introductory Remarks. My main purpose in this paper is to prove a bifurcation theorem for nontrivial periodic solutions of a general system of Volterra integral equations. The motivation for considering this problem can be found in models which arise in population dynamics, epidemiology and economics [1,3,6], an example of which appears in §5. The approach taken is that which is usually refe...

Exact solutions of nonlinear interval Volterra integral equations

Periodic solutions of discrete Volterra equations

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...

Solutions for Singular Volterra Integral Equations

0 gi(t, s)[Pi(s, u1(s), u2(s), · · · , un(s)) + Qi(s, u1(s), u2(s), · · · , un(s))]ds, t ∈ [0, T ], 1 ≤ i ≤ n where T > 0 is fixed and the nonlinearities Pi(t, u1, u2, · · · , un) can be singular at t = 0 and uj = 0 where j ∈ {1, 2, · · · , n}. Criteria are offered for the existence of fixed-sign solutions (u∗1, u ∗ 2, · · · , u ∗ n) to the system of Volterra integral equations, i.e., θiu ∗ i (...

Periodic Solutions of Periodic Delay Lotka Volterra Equations and Systems

By using the continuation theorem of coincidence degree theory, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic Lotka Volterra equations and systems with distributed or statedependent delays. Our results substantially extend and improve existing results. 2001 Academic Press