The nonlinear Kneser problem for singular in phase variables second-order differential equations

Abstract

For the singular in phase variables differential equation u'' = f (t, u, u') ), sufficient conditions are found for the existence of a solution satisfying the conditions Phi(u) = c, u(t) > 0, u'(t) < 0 for t > 0, where Phi : C([0, a]; R+) to R+ is a continuous nondecreasing functional, c > 0, and a > 0.For the singular in phase variables differential equation u'' = f (t, u, u') ), sufficient conditions are found for the existence of a solution satisfying the conditions Phi(u) = c, u(t) > 0, u'(t) < 0 for t > 0, where Phi : C([0, a]; R+) to R+ is a continuous nondecreasing functional, c > 0, and a > 0.