Abstract We study the eigenvalue problem for a superlinear convolution operator in special case of bilinear constitutive laws and establish existence uniqueness one-parameter family nonlinear eigenfunctions under topological shape constraint. Our proof uses change scalar parameters applies Krein–Rutman arguments to linear substitute problem. also present numerical simulations discuss asymptotic...

We study the spectral stability of small-amplitude periodic traveling waves Ostrovsky equation. prove that these exhibit instabilities arising from a collision pair non-zero eigenvalues on imaginary axis when subjected to square-integrable perturbations whole real line. also list all such collisions between pairs and do Krein signature analysis.