One-Parameter Families of Positive Solutions of Some Classes of Nonlinear Convolution Type Integral Equations

We consider a class of nonlinear convolution type integral equations with a noncompact Hammerstein operator on the half-line and on the whole line. Under certain conditions on nonlinearity, we prove the existence of a one-parameter family of positive solutions and study the asymptotic behavior of the solutions at infinity. The results are illustrated by examples of the equations under consideration.