Extremal solutions for nonlinear neumann problems

• Autorzy: Antonella Fiacca , Raffaella Servadei
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.

Słowa kluczowe

EN

upper solution; lower solution; order interval; truncation function; penalty function; pseudomonotone operator; coercive operator; extremal solution

Kategorie tematyczne

• 35J65: Nonlinear boundary value problems for linear elliptic equations
• 35J60: Nonlinear elliptic equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 191-206

Daty

wydano

2001

otrzymano

2001-07-07

Twórcy

autor

Antonella Fiacca

• University of Perugia, Department of Mathematics and Computer Science, via Vanvitelli 1, Perugia 06123 Italy

autor

Raffaella Servadei

• University of Perugia, Department of Mathematics and Computer Science, via Vanvitelli 1, Perugia 06123 Italy
• University of Roma 2, Department of Mathematics, via della Ricerca Scientifica, Roma 00133 Italy

Bibliografia

• [1] R. Adams, Sobolev Spaces, Academic Press, New York 1975.
• [2] R.B. Ash, Real Analysis and Probability, Academic Press, New York, San Francisco, London 1972.
• [3] H. Brézis, Analyse Functionelle: Théorie et Applications, Masson, Paris 1983.
• [4] F.E. Browder and P. Hess, Nonlinear Mappings of Monotone Type in Banach Spaces, J. Funct. Anal. 11 (1972), 251-294.
• [5] T. Cardinali, N.S. Papageorgiou and R. Servadei, The Neumann Problem for Quasilinear Differential Equations, preprint.
• [6] E. Casas and L.A. Fernández, A Green's Formula for Quasilinear Elliptic Operators, J. Math. Anal. Appl. 142 (1989), 62-73.
• [7] E. Dancer and G. Sweers, On the Existence of a Maximal Weak Solution for a Semilinear Elliptic Equation, Diff. Integral Eqns 2 (1989), 533-540.
• [8] J. Deuel and P. Hess, A Criterion for the Existence of Solutions of Nonlinear Elliptic Boundary Value Problems, Proc. Royal Soc. Edinburgh (A) 74 (1974-75), 49-54.
• [9] N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory, Interscience Publishers, New York 1958-1971.
• [10] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin 1983.
• [11] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York 1975.
• [12] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis. Volume I: Theory, Kluwert, Dordrecht, The Netherlands 1997.
• [13] N. Kenmochi, Pseudomonotone Operators and Nonlinear Elliptic Boundary Value Problems, J. Math. Soc. Japan 27 (1975), 121-149.
• [14] J. Leray and J.L. Lions, Quelques Resultats de Visik sur les Problems Elliptiques Nonlinearities par Methodes de Minty-Browder, Bull. Soc. Math. France 93 (1965), 97-107.
• [15] J.J. Nieto and A. Cabada, A Generalized Upper and Lower Solutions Method for Nonlinear Second Order Ordinary Differential Equations, J. Appl. Math. Stochastic Anal. 5 (2) (1992), 157-165.
• [16] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990.

Identyfikatory

DOI

10.7151/dmgt.1024