Abstract
Let \( \Upomega \) be a bounded domain in RN, and \( {\text{Lu}} = \sum\nolimits_{\left| \upalpha \right| \le \text{m}\;\left| \upbeta \right| \le \text{m}} {( - 1)^{\left| \upbeta \right|} \text{D}^{\upbeta } } (\text{a}_{\upalpha \upbeta } (\text{x})\text{D}^{\upalpha }\text{u}) \) be a uniformly strongly elliptic operator acting on functions defined in \( \Upomega \).
The material presented here corresponds roughly to the lectures given by Djairo Guedes de Figueiredo at Tulane, in a program sponsored by the Ford Foundation.
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REFERENCES
ADAMS, R.A., A quasi-line or elliptic boundary value problem, Canad. J. Math. 18 (1966), 1105-1112.
DE FIGUEIREDO, D. G., Some remarks on the Dirichlet Problem for semilinear elliptic equations, Anais Acad. Brasil. Ci., to appear.
DE FIGUEIREDO, D. G., On the range of nonlinear operators with linear asymptotes which are not invertible, Comm. Math. Univ. Carolinae, to appear.
FRIEDMAN, A., Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.
FUČIK, KUČERA, NEČAS, Ranges of nonlinear asymptotically linear operators, to appear.
HESS, P., On a theorem by Landesman and Lazer, Indiana U. Math. J. 23 (1974), 827-829.
KRASNOSELSKII, M. A., Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, New York, 1964.
LANDESMAN, E. M., and Lazer, A. C, Linear eigen values and a nonlinear boundary value problem, Pacific J. Math. 33 (1970), 311-328.
LANDESMAN, E. M., and LAZER, A. C., Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623.
NEČAS, J., On the range of nonlinear operators with linear asymptotes which are not invertible, Comm. Math. Univ. Carolinae 14 (1973), 63-72.
NIRENBERG, L., An application of generalized degree to a class of nonlinear problems, Proc. Symp. Fctl. Anal. Liège, Sept, 1971.
SHULTZ, M. H., Quasi-linear elliptic boundary value problems, J. Math. Mech. 18 (1968), 21-25.
VAINBERG, M., Variational Methods for the Study of Nonlinear Operators, Holden Day, San Francisco, 1964.
WILLIAMS, S. A., A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Diff. Eq. 8 (1970), 580-586.
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de Figueiredo, D.G. (1975). The Dirichlet Problem for Nonlinear Elliptic Equations: A Hilbert Space Approach. In: Costa, D. (eds) Djairo G. de Figueiredo - Selected Papers. Springer, Cham. https://doi.org/10.1007/978-3-319-02856-9_6
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DOI: https://doi.org/10.1007/978-3-319-02856-9_6
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