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1991-1992 | 56 | 1 | 49-61
Tytuł artykułu

Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper treats nonlinear elliptic boundary value problems of the form
(1) L[u] = p(x,u) in $Ω ⊂ ℝ^n$, $u = Du = ... = D^{m-1}u$ on ∂Ω
in the Sobolev space $W_0^{m,2}(Ω)$, where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.
Słowa kluczowe
Rocznik
Tom
56
Numer
1
Strony
49-61
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-04-02
poprawiono
1991-03-02
Twórcy
autor
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [1] H. Amann and S. A. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39-54.
  • [2] A. Ambrosetti and G. Mancini, Sharp nonuniqueness results for some nonlinear problems, Nonlinear Anal. 3 (1979), 635-645.
  • [3] A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
  • [4] K.-C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
  • [5] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York 1969.
  • [6] L. Gå rding, Dirichlet's problem for linear elliptic partial differential equations, Math. Scand. 1 (1953), 55-72.
  • [7] E. M. Landesman and A. C. Lazer, Linear eigenvalues and a nonlinear boundary value problem, Pacific J. Math. 33 (1970), 311-328.
  • [8] A. C. Lazer and P. J. McKenna, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl. 84 (1981), 282-294.
  • [9] L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute of Mathematical Sciences, New York University, 1974.
  • [10] R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165-171.
  • [11] W. V. Petryshyn, Variational solvability of quasilinear elliptic boundary value problems at resonance, Nonlinear Anal. 5 (1981), 1095-1108.
  • [12] P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, R.I., 1986.
  • [13] M. Struve, A note on a result of Ambrosetti and Mancini, Ann. Mat. Pura Appl. 131 (1982), 107-115.
  • [14] M. Vaĭnberg, On the continuity of some operators of special type, Dokl. Akad Nauk SSSR 73 (1950), 253-255 (in Russian)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv56z1p49bwm
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