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On the solvability of one class of nonlinear integral equations in L 1(0,+∞)

Abstract

We study the problem of constructing a solution that is positive, integrable, and essentially bounded on (0,+∞) to one class of nonlinear Hammerstein integral equations with noncompact operator in the critical case.

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Correspondence to K. A. Khachatryan.

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Original Russian Text © K.A. Khachatryan and T.E. Terdzhyan, 2015, published in Matematicheskie Trudy, 2015, Vol. 18, No. 12, pp. 190–200.

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Khachatryan, K.A., Terdzhyan, T.E. On the solvability of one class of nonlinear integral equations in L 1(0,+∞). Sib. Adv. Math. 25, 268–275 (2015). https://doi.org/10.3103/S1055134415040045

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Keywords

  • nonlinear equation
  • Hammerstein operator
  • space of integrable functions
  • convergence
  • monotonicity