We consider here a class of nonlinear Dirichlet problems, in a bounded domain Omega of the form { -div(a(x, u)delu) + div(Phi(u)) = f in Omega, u = 0 on thetaOmega, investigating the problem of uniqueness of solutions. The functions Phi(s) and s --> a(x, s) satisfy rather general assumptions of locally Lipschitz continuity (with possibly exponential growth) and the datum f is in L-1(Omega). Uniqueness of solutions is proved both for coercive a(x, s) and for the case of a(x, s) degenerating for s large.
Porretta, A. (2004). Uniqueness of solutions for some nonlinear Dirichlet problems. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 11(4), 407-430 [10.1007/s00030-004-0031-y].
Uniqueness of solutions for some nonlinear Dirichlet problems
PORRETTA, ALESSIO
2004-01-01
Abstract
We consider here a class of nonlinear Dirichlet problems, in a bounded domain Omega of the form { -div(a(x, u)delu) + div(Phi(u)) = f in Omega, u = 0 on thetaOmega, investigating the problem of uniqueness of solutions. The functions Phi(s) and s --> a(x, s) satisfy rather general assumptions of locally Lipschitz continuity (with possibly exponential growth) and the datum f is in L-1(Omega). Uniqueness of solutions is proved both for coercive a(x, s) and for the case of a(x, s) degenerating for s large.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
