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On the existence of solutions for quadratic integral equations on unbounded intervals for quasibounded maps

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Citations From References: 0 From Reviews: 0 MR3601848 45G10 45D05 47H30

Anichini, G.[Anichini, Giuseppe](I-FRNZ-MCS); Conti, G.[Conti, Giuseppe](I-FRNZ-MCS)

On the existence of solutions for quadratic integral equations on unbounded intervals for quasibounded maps. (English summary)

Rend. Semin. Mat. Univ. Politec. Torino72 (2014),no. 3-4,151–160. The authors study the solvability of a nonlinear quadratic integral equation

x(t) = f (t) + (Ax)(t) t Z

t0

k(t, s)F (s, x(s))ds, t ∈ J = [0, +∞),

in the Fr´echet space C(J,R), where A: C(J,R) → C(J,R) is a continuous operator such

that

|A(x)(t)| ≤ a|x(t)|, t ∈ J,

and its restrictions to (C([0, n],R), k · kn) satisfy the Darbo property with a positive constant kn.

Under suitable conditions, using a fixed point result for condensing acyclic multivalued operators, they prove the existence of a solution in C(J,R). An illustrative example is

also given. Marcel-Adrian S¸erban

c

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