Hammerstein-Nemytskii type nonlinear integral equations on half-line in space \(L_1(0,+\infty )\cap L_{\infty}(0,+\infty)\). (English) Zbl 1290.45001

Khachatryan, Aghavard Kh.; Khachatryan, Khachatur A.

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 52, No. 1, 89-100 (2013).

The questions of solvability and uniqueness of the following class of Hammerstein-Nemytskii type nonlinear integral equations as \[ \varphi(x) = A(x,\varphi(x)) + \int\limits_0^\infty k(x-t) B(t,\varphi(t))dt, \, x \geq 0, \] with noncompact integral operator are discussed. Kernel \(K \in L_1(0,\infty) \bigcap L_\infty(0,\infty)\). This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results.

Reviewer: Ilia V. Boikov (Penza)

MSC:

45G05	Singular nonlinear integral equations
47H30	Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)

Keywords:

Wiener-Hopf operator; Hammerstein-Nemytskii equation; nonlinear integral equations; noncompact integral operator

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