The book reviews some recent results on global solution curves and exact multiplicity of positive solutions for the semilinear dirichlet problem on a bounded domain dhere u ux x d r n . We study curves of positive solutions for a system of elliptic equations of hamiltonian type on a unit ball we give conditions for all positive solutions to lie on global solution curves . Positive solutions for a class of semilinear elliptic systems 93 obtain the precise global bifurcation diagrams of the system and the bifurcation diagram is a single monotone solution curve in all cases. Global solution curves for semilinear systems we study semilinear elliptic systems in two dierent directions in the rst one we give a simple constructive proof of existence of solutions for a class of sublinear systems our main results are in wewould concludefrom thesecond equation in 2 that. We obtain precise global bifurcation diagrams for both one sign and sign changing solutions of a semilinear elliptic equation for the nonlin see 15 we obtain a full description of the rstnsolution curves which bifurcate from the line of trivial solutions to state our results we rst introduce some notation
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