In this article, we give a new proof of the existence of bounded solutions for the problem {-div(M(x, u)Du) + mu u = B(x, u, Du) + f(x) in Omega, u=0 on partial derivative Omega using the method introduced in Boccardo et al. [Existence de solutions non bornees pour certaines equations quasi lineaires, 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.
The Fatou lemma approach to the existence in quasilinear elliptic equations with natural growth terms / Boccardo, Lucio. - In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. - ISSN 1747-6933. - 55:5-6(2010), pp. 445-453. [10.1080/17476930903276241]
The Fatou lemma approach to the existence in quasilinear elliptic equations with natural growth terms
BOCCARDO, Lucio
2010
Abstract
In this article, we give a new proof of the existence of bounded solutions for the problem {-div(M(x, u)Du) + mu u = B(x, u, Du) + f(x) in Omega, u=0 on partial derivative Omega using the method introduced in Boccardo et al. [Existence de solutions non bornees pour certaines equations quasi lineaires, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
