Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The paper investigates the nonlinear partial differential equations of the superlinear elliptic type with the Dirichlet boundary data. Some sufficient conditions, under which the solutions of considered equations depend continuously on distributed and boundary controls, are proved. The proofs of the main results are based on variational methods.
Czasopismo
Rocznik
Tom
Strony
987--1004
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Faculty of Mathematics, University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Poland, bors@math.uni.Iodz.pl
Bibliografia
- Adams, R.A. (1975) Sobolev Spaces. Academic Press, New York.
- Courant, R. and Hilbert, D. (1962) Methods of Mathematical Physics. Wiley Interscience, New York.
- Evans, L.C. (1998) Partial Differential Equations. American Mathematical Society, Providence, Rhode Island.
- Ingram, S.K. (1972) Continuous dependence on parameters and boundary data for nonlinear two-point boundary value problems. Pacific J. Math. 41, 395-408.
- Kok, B. and Penning, F.D. (1980/81) Continuous dependence of the solutions of elliptic boundary value problems on the coefficients, right hand sides and boundary conditions. Quaestiones Math. 4 (3), 167-183.
- Klaasen, G. (1970) Dependence of solutions on boundary conditions for second order ordinary differential equations. J. Diff. Equations 7, 24-33.
- Kufner, A., John, O. and Fucik, S. (1977) Function Spaces. Academia, Prague.
- Lepin, A. and Ponomariev, W. (1973) Continuous dependence of solutions of the boundary value problem for ordinary differential equations (in Russian). Differential Equations 9, 626-629.
- Macki, J. and Strauss, A. (1982) Introduction to Optimal Control Theory. Springer-Verlag, New York-Heidelberg-Berlin.
- Mawhin, J. (1987) Problemes de Dirichlet Variationnels Non-Lineaires. Les Presses de L′Universite de Montreal, Canada (see also, Polish edition: WNT 1994 Warszawa).
- Mawhin, J. and Willem, M. (1989) Critical Point Theory and Hamiltonian Systems. Springer-Verlag, New York.
- Oleinik, O.A. (1952) On properties of solutions of certain boundary problems for equations of elliptic type. Mat. Sbornik N.S. 30 (72), 695-702.
- Rabinowitz, P.H. (1986) Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Regional Conference Series Math. 65, Amer. Math. Soc., Providence.
- Sedziwy, S. (1971) Dependence of solutions on boundary data for a system of two ordinary differential equations. J. Differential Equations 9, 381-389.
- Struwe, M. (1990) Variational Methods. Springer-Verlag.
- Walczak, S. (1995) On the continuous dependence on parameters of solutions of the Dirichlet problem. Bulletin de la Classe des Sciences de l′Academie Royale de Belgique, 7-12, 247-273.
- Walczak, S. (1998) Continuous dependence on parameters and boundary data for nonlinear PDE. Coercive case. Differential and Integral Equations 11 (1), 35-46.
- Willem, M. (1996) Minimax Theorems. Birkhauser, Boston.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0010-0012