Existence and Boundedness of Solutions for Systems of First Order Nonlinear Differential Equations
Mubarak, Abdulrahman A. M. A.
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In this thesis we discuss the classification, continuablity, existence, and boundedness of monotonic solutions for the system of first order nonlinear differential equations in the form x'(t) = p(t)f(y(t)), y'(t) = q(t)g(x(t)). First we prove that all solutions of the system are eventually monotonic and can be classified into four classes. Then we consider the continuability of all solutions and obtain the result that all solutions of the system can be extended under some natural assumptions. After that, we discuss the boundedness of all solutions. Finally, we establish the existence of solutions in two subclasses. The results obtained in this thesis have generalized and improved some analogous ones existing in the literature.