Displaying similar documents to “On a fixed point theorem of Krasnoselskii-Schaefer type.”

Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici


A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.

On monotonic solutions of an integral equation of Abel type

Mohamed Abdalla Darwish (2008)

Mathematica Bohemica


We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C [ 0 , 1 ] . The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.