Solutions for Singular Volterra Integral Equations
نویسندگان
چکیده
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 (t) ≥ 0 for t ∈ [0, 1] and 1 ≤ i ≤ n, where θi ∈ {1,−1} is fixed. We also include an example to illustrate the usefulness of the results obtained.
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