Existence of nontrivial solutions of certain linear and nonlinear convolution-type equations

Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

“…The solubility of (1.1) and asymptotic properties of the resulting solutions were first studied in [16] under the following restrictions on the kernel of the equation: and under the assumption that H(t, u) can be represented in the form H(t, u) = u − ω(u), (1.6) where ω ∈ L 1 (R + ) ∩ C 0 (R + ), ω ↓ in u on a certain semi-infinite interval [δ, +∞), δ > 0. Here C 0 (R + ) stands for the space of continuous functions on R + with zero limit at infinity.…”

Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

“…В работе [16] впервые были обсуждены вопросы разрешимости уравнения (1.1) и изучены асимптотические свойства полученных решений в предположении, что ядро уравнения удовлетворяет следующим условиям:…”