Browsing by Author "Mershaye, Dagmawit"

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    Multiplicity of Positive Solutions and the Method of Upper and Lower Solutions for Nonlinear Elliptic Pdes
    (Addis Ababa University, 2021-10-19) Mershaye, Dagmawit; Abdi, Tadesse (PhD)
    In this paper, we are interested in the positive solutions of nonlinear elliptic boundary value problems on a bounded domain. We establish the existence, uniqueness and multiplicity of positive solutions for the nonlinear elliptic boundary value problem of autonomous type, ( 􀀀Lu = f (x, u) in W Bu = c(x) on ¶W and then proceed to establish conditions for existence and uniqueness of positive global solutions for the non-autonomous type elliptic BVP, 8>< >: ut 􀀀4u = f (x, t, u) in D Bu = c(x, t) on ¶D u(x, 0) = u0(x) in W We employ the method of lower and upper solutions along with the monotone iterative techniques to this end.