He discusses in detail the Dirichlet problems
for quasilinear and fully nonlinear elliptic equations of the second order: quasilinear uniformly elliptic equations in arbitrary domains, mean curvature equations in domains with non-negative boundary mean curvature, fully nonlinear uniformly elliptic equations in arbitrary domains, and Monge-Ampere equation in uniformly convex domains.
N, and then performs the following two-step iteration: at each iteration k, one first solves Dirichlet problems
on each [[OMEGA].
Two kinds of Dirichlet problems
are usually considered for biharmonic equation (1).
Papageorgiou, Dirichlet problems
with an indefinite and unbounded potential and concave-convex nonlinearities, Abstr.
The Dirichlet problems
for higher-order linear differential equations in multiply connected domains have not been solved yet.
The existence of solutions of p(x)-Laplacian Dirichlet problems
has been studied in many papers (see e.
There are many papers devoted to the Dirichlet problems
of quasilinear elliptic equations, see for example , , .
2005, A numerical method to find a positive solution of semilinear elliptic Dirichlet problems
, Applied Mathematics and Computation, Article in Press.
Evaluation of The Di_erence Between The Regularizators of Di_raction and of Dirichlet Problems
Neuberger, A Reduction Algorithm for Sublinear Dirichlet Problems
, Nonlinear Analysis, 47 (2001), 33793390.
Profile graphs of the values for relative elapsed time changes [Delta]T for the mixed and Neumann problems with respect to the Dirichlet problems
Passaseo, Nonlinear elliptic Dirichlet problems
in exterior domains: the role of geometry and topology of the do-main, Comm.