A Contribution to the Theory of Quasilinear Elliptic Equations and Application to the Minimization of Integral Functionals

The aim of this work is to study the existence of solutions of quasilinear elliptic problems of the type

$left{{ll}-{rm div}([a(x) + |u|^q] nabla u) + b(x)u|u|^{p-1}|nabla u|^2 = f(x), & {rm in},Omega; quad quad quad quad quad quad quad quad quad ; u = 0, & ,{rm on},partialOmega. right.$left{begin{array}{ll}-{rm div}([a(x) + |u|^q] nabla u) + b(x)u|u|^{p-1}|nabla u|^2 = f(x), & {rm in},Omega; quad quad quad quad quad quad quad quad quad ; u = 0, & ,{rm on},partialOmega. end{array}right.
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