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My doctoral dissertation, "Solvability of Nonlinear Elliptic Boundary Value Problems," focused on the study of steady states of reaction-diffusion problems motivated by real-world applications. The research centered on two complementary areas: elliptic boundary value problems with nonlinear reactions appearing either in the interior or on the boundary of domains. I established existence results for maximal and minimal solutions using monotone iteration methods and degree theory, extended classical theory to systems with nonlinear boundary conditions, and developed numerical approximation methods using finite difference techniques. Additionally, I investigated mathematical models arising in ecology, particularly studying competition and cooperation dynamics between species in fragmented habitats. This comprehensive work bridged pure mathematical theory with computational applications and ecological modeling, contributing to both theoretical advances in nonlinear analysis and practical insights for population dynamics in heterogeneous environments.