Multiple Solutions Of Strong Moulineat Elliptic Problems

In this doctoral thesis we study the existence and multiplicityy of solutions of strong nonlinear elliptic problems including eritical or supercritical case,elliptic operator different fromâ–³p and elliptic equation with nonlinear boundary condi-tions.The first is about the elliptic Dirichlet problem with a critical or supercritical term (?)(?)(?) where Ω is a bounded smooth domain of RV,â–³pu=div(|(?))is the p-Laplacian,1<p<N,N≥3,r≥p*=Np/N-p.λ,u are nonnegative constants,and f:Ω×Râ†'R is a Caratheodory function.Three weak solutions of the problem (P1)are obtained by a three critical points theorem of B.Ricceri combinning with the technique of truncation and the Moser iteration.The second elliptic problem is the no-flux problem with nonlinear elliptic operat or wherr Ω is a bounded smooth domain of RN.We obtain at least two trivial solutions of the problem (P2) by the mountaion pass lemma under some assumptions for the quasilinear elliptie operator a(x,(?))and nonlinear term f.The last problem is the following ellipite equation with nonliuear boundary condition where Ω is a bounded smooth domain of RN and (?) is the outward unit normal on (?)Ω.Using vatiational methods based on the critcal point theory and Morse theory. combining with the sub-supersolutuions methods and the technique of truncation. we show that the problem (P3)has at least six nontruvial solutions...