In this paper we study the existence of bounded weak solutions in unbounded domains for some nonlinear Dirichlet problems. The principal part of the operator behaves like the $p$-laplacian operator, and the lower order terms, which depend on the solution $u$ and its gradient $\D u$, have a power growth of order $p-1$ with respect to these variables, while they are bounded in the $x$ variable. The source term belongs to a Lebesgue space with a prescribed asymptotic behaviour at infinity.
Existence of bounded solutions for nonlinear elliptic equations in unbounded domains / Dall'Aglio, Andrea; DE CICCO, Virginia; Giachetti, Daniela; J. P., Puel. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 11:4(2004), pp. 431-450. [10.1007/s00030-004-1070-0]
Existence of bounded solutions for nonlinear elliptic equations in unbounded domains
DALL'AGLIO, Andrea;DE CICCO, Virginia;GIACHETTI, Daniela;
2004
Abstract
In this paper we study the existence of bounded weak solutions in unbounded domains for some nonlinear Dirichlet problems. The principal part of the operator behaves like the $p$-laplacian operator, and the lower order terms, which depend on the solution $u$ and its gradient $\D u$, have a power growth of order $p-1$ with respect to these variables, while they are bounded in the $x$ variable. The source term belongs to a Lebesgue space with a prescribed asymptotic behaviour at infinity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
