Multiplicity Of Positive Solutions And The Method Of Upper And Lower Solutions For Nonlinear Elliptic Pdes

In this paper, we are interested in the positive solutions of nonlinear ellipticrnboundary value problems on a bounded domain. We establish the existence,rnuniqueness and multiplicity of positive solutions for the nonlinear ellipticrnboundary value problem of autonomous type,rn(rnÀ€€Lu = f (x, u) in WrnBu = c(x) on ¶Wrnand then proceed to establish conditions for existence and uniqueness of positivernglobal solutions for the non-autonomous type elliptic BVP,rn8>:rnut ð€€€4u = f (x, t, u) in DrnBu = c(x, t) on ¶Drnu(x, 0) = u0(x) in WrnWe employ the method of lower and upper solutions along with the monotonerniterative techniques to this end.

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