Abstract
In this article, we give a new proof of the existence of bounded solutions for the problem using the method introduced in Boccardo et al. [Existence de solutions non bornèes pour certaines equations quasi linèaires, Portugaliae Math. 41 (1982), pp. 507–534] and developed in Boccardo [Dirichlet problems with singular and gradient quadratic lower order terms, ESAIM: Control. Optim. Calc. Var. 14 (2008), pp. 411–426], even if here we do not assume a sign condition on the quadratic lower order term B(x, u, Du). A case yielding unbounded solutions will be studied as well.
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