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On the existence of solutions of $$-\Delta u=g(x,u,\nabla u)$$. (English) Zbl 0598.35041
The author studies the existence and the uniqueness of the weak solutions of the nonlinear elliptic Dirichlet problems satisfying a nonresonance condition. He extends a result of D. G. de Figueiredo [Lect. Notes Math. 446, 144-165 (1975; Zbl 0312.35032)]. The main results are obtained using constructive proofs (for instance, the fixed point theorem of Banach).
Reviewer: D.Ştefănescu

##### MSC:
 35J35 Variational methods for higher-order elliptic equations 35D05 Existence of generalized solutions of PDE (MSC2000)