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