QUASILINEAR ODE WITH MEASURE DATA

Abstract

In the thesis the author studies a family of quasilinear ODEs of Sturm-Liouville type with a general parameter p. By appealing to theory of monotone operators and method of calculus of variation, he proves that a condition is equivalent to the existence and uniqueness of weak solutions to every ODE in such a family. He also extends the result to a family of more general ODEs. At last, he establishes some regularity and compactness results that may have independent interest.