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Quasilinear elliptic equations with quadratic growth in unbounded domains. (English) Zbl 0602.35036
Die Autorinnen untersuchen das Dirichletproblem für nichtlineare elliptische Gleichungen der Form \[ -\sum_{i,j}(\partial /\partial x_ j)a_{ij}(x,u)\partial /\partial x_ j+f(x,u,\text{grad} u)=0 \] in einer unbeschränkten Menge \(\Omega \subset {\mathbb{R}}^ n\). Unter Wachstumsvoraussetzungen an die Nichtlinearität wird Existenz einer Lösung bewiesen.
Reviewer: W.Wendt

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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[1] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solution of elliptic partial differential equations satisfying general boundary conditions, Communs pure appl. math., 12, 623-727, (1959), I · Zbl 0093.10401
[2] Amann, H.; Crandall, M.G., On some existence theorems for semilinear elliptic equations, Indiana univ. math. J., 27, 779-790, (1978) · Zbl 0391.35030
[3] Bensoussan, A.; Freshe, J., Nonlinear elliptic systems in stochastic game theory, J. reine angew. math., 350, 23-67, (1984) · Zbl 0531.93052
[4] Benci, V.; Fortunato, D., Some nonlinear elliptic problems with asymptotic conditions, Nonlinear analysis, 3, 157-174, (1979) · Zbl 0404.35043
[5] Boccardo, L.; Murat, F.; Puel, J.L., Existence de solutions faibles pour des equations elliptiques quasilinéaires à croissance quadratique, (), 19-73, Research Notes in Mathematics
[6] Boccardo, L.; Murat, F.; Puel, J.L., Résultats d’existence pour certains problèmes elliptiques quasi-linéaires, Annali scu. norm. sup. Pisa, XI, Ser. IV, 213-235, (1984) · Zbl 0557.35051
[7] Boccardo L., Murat F. & Puel J.P., Existence of bounded solutions for nonlinear elliptic unilateral problems (to appear). · Zbl 0687.35042
[8] Các, N.P., Nonlinear elliptic boundary value problems for unbounded domains, J. diff. eqns, 45, 191-198, (1982) · Zbl 0508.35032
[9] Các, N.P., On some quasilinear elliptic boundary value problems with conditions at infinity, J. diff. eqns, 52, 342-355, (1984) · Zbl 0543.35037
[10] Donato, P.; Migliaccio, L.; Schianchi, R., Semilinear elliptic equations in unbounded domains of \(R\)^n, Proc. R. soc. edinb., 88A, 109-119, (1981) · Zbl 0456.35033
[11] Freshe, J., On the regularity of solutions to elliptic differential inequalities, (), Annals of Ceremade
[12] Gilbarg, D.; Trudinger, N.S., Elliptic partial differential equation of second order, (1977), Springer Berlin · Zbl 0691.35001
[13] Hess, P., Nonlinear elliptic problems in unbounded domains, Abhandlung der akademie des wissenschafter der D.D.R., (1975), International Summer School in Nonlinear Operator. Berlin, September 1975
[14] Ladyzhenskaya, O.A.; Uralt’seva, N., Linear and quasilinear elliptic equations, (1968), Academic Press New York
[15] Leray, J.; Lions, J.L., Quelques résultats de visik sur LES problèmes elliptiques non linéaires par LES methodes de minty-Browder, Bull. soc. math. France, 93, 97-107, (1965) · Zbl 0132.10502
[16] Lions, J.L., Quelques Méthodes de Résolutions des problèmes aux limites non linéaires, (1969), Dunod Paris · Zbl 0189.40603
[17] Miranda, C., Su alcuni teoremi di inclusione, Annales polonici mathematici, XVI, 305-315, (1965) · Zbl 0172.40303
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