Solvability of Dirichlet problem for a class of degenerate anisotropic equations with L1-right-hand sides

We study Dirichlet problem for a class of degenerate anisotropic nonlinear elliptic fourth order equations with L-1-right-hand sides. Anisotropic and degenerate character of the equations under consideration is expressed by the presence in their coefficients of different exponents and weighted functions associated to the first and second order derivatives of unknown function. Under some hypotheses on the involved exponents and weighted functions we prove existence of so-called H-v,H-mu-solution and H-solution of the given problem. (C) 2004 Elsevier Ltd. All rights reserved.