Zero-convergent solutions for equations with generalized relativistic operator: a fixed point approach.

A new abstract fixed point theorem is presented and applied to the solvability of a boundary value problem on the half-line for a differential equation with the generalized relativistic operator. The method does not require the explicit form of the fixed point map and can be applied also for solving boundary value problems associated to equations with various types of non-homogeneous operators. The concept of principal solutions for half-linear equations is also used for finding suitable a-priori bounds for solutions.