| Summary: | <p>In this dissertation, we establish new existence, multiplicity, and uniqueness results on
positive radial solutions for classes of steady state reaction diffusion equations on the exterior
of a ball. In particular, for the first time in the literature, this thesis focuses on the
study of solutions that satisfy a general class of nonlinear boundary conditions on the interior
boundary while they approach zero at infinity (far away from the interior boundary).
Such nonlinear boundary conditions occur naturally in various applications including models
in the study of combustion theory. We restrict our analysis to reactions terms that grow
slower than a linear function for large arguments. However, we allow all types of behavior
of the reaction terms at the origin (cases when it is positive, zero, as well as negative). New
results are also added to ecological systems with Dirichlet boundary conditions on the interior
boundary (this is the case when the boundary is cold). We establish our existence and
multiplicity results by the method of sub and super solutions and our uniqueness results
via deriving a priori estimates for solutions.</p>
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