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1993 | 66 | 1 | 109-12
Tytuł artykułu

Three methods for the study of semilinear equations at resonance

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.
Słowa kluczowe
Rocznik
Tom
66
Numer
1
Strony
109-12
Opis fizyczny
Daty
wydano
1993
otrzymano
1993-03-08
Twórcy
  • Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] A. R. Abdullaev and A. B. Burmistrova, On the solvability of boundary value problems at resonance, Differentsial'nye Uravneniya 25 (1989), 2044-2048.
  • [2] A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Math. Pura Appl. 93 (1973), 231-247.
  • [3] H. Brézis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa 5 (1978), 225-326.
  • [4] L. Cesari, Functional analysis, nonlinear differential equations, and the alternative method, in: Nonlinear Functional Analysis and Differential Equations, L. Cesari, R. Kannan and J. D. Schuur (eds.), Dekker, New York, 1976, 1-197.
  • [5] D. G. de Figueiredo, On the range of nonlinear operators with linear asymptotes which are not invertible, Comment. Math. Univ. Carolinae 15 (1974), 415-428.
  • [6] K. Deimling, Nonlinear Functional Analysis, Springer, 1985.
  • [7] P. Drábek, Landesman-Lazer type condition and nonlinearities with linear growth, Czechoslovak Math. J. 40 (1990), 70-87.
  • [8] P. Drábek, Landesman-Lazer condition for nonlinear problems with jumping nonlinearities, J. Differential Equations, to appear.
  • [9] S. Fučik, Nonlinear equations with noninvertible linear part, Czechoslovak Math. J. 24 (1974), 259-271.
  • [10] S. Fučik, Solvability of Nonlinear Equations and Boundary Value Problems, Reidel, Dordrecht, 1980.
  • [11] R. E. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Math. 568, Springer, 1977.
  • [12] P. Hess, On a theorem by Landesman and Lazer, Indiana Univ. Math. J. 23 (1974), 827-829.
  • [13] R. Iannacci and M. N. Nkashama, Nonlinear two point boundary value problem at resonance without Landesman-Lazer condition, Proc. Amer. Math. Soc. 106 (1989), 943-952.
  • [14] R. Iannacci and M. N. Nkashama, Unbounded perturbations of forced second order ordinary differential equations at resonance, J. Differential Equations 69 (1987), 289-309.
  • [15] R. Iannacci, M. N. Nkashama and J. R. Ward, Nonlinear second order elliptic partial differential equations at resonance, Trans. Amer. Math. Soc. 311 (1989), 710-727.
  • [16] R. Kannan, Perturbation methods for nonlinear problems at resonance, in: Nonlinear Functional Analysis and Differential Equations, L. Cesari, R. Kannan and J. D. Schuur (eds.), Dekker, New York, 1976, 209-225.
  • [17] E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623.
  • [18] N. G. Lloyd, Degree Theory, Cambridge Univ. Press, Cambridge, 1978.
  • [19] J. Mawhin, Topological degree methods in nonlinear boundary value problems, Regional Conf. Series in Math. 40, Amer. Math. Soc., Providence, R.I., 1979.
  • [20] J. Mawhin, Boundary value problems for vector second order nonlinear ordinary differential equations, in: Lecture Notes in Math. 703, Springer, 1979, 241-249.
  • [21] L. C. Piccinini, G. Stampacchia and G. Vidossich, Ordinary Differential Equations in $ℝ^n$, Appl. Math. Sci. 39, Springer, 1984.
  • [22] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43.
  • [23] B. Przeradzki, Operator equations at resonance with unbounded nonlinearities, preprint.
  • [24] B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl., to appear.
  • [25] B. Przeradzki, A note on solutions of semilinear equations at resonance in a cone, Ann. Polon. Math. 58 (1993), 95-103.
  • [26] B. Przeradzki, The solvability of nonlinear equations with noninvertible linear part, Acta Univ. Lodzensis, habilitation thesis.
  • [27] B. Przeradzki, Nonlinear boundary value problems at resonance for differential equations in Banach spaces, preprint.
  • [28] B. Ruf, Multiplicity results for nonlinear elliptic equations, in: Nonlinear Analysis, Function Spaces and Applications, Vol. 3 (Litomyšl 1986), Teubner-Texte zur Math. 93, Teubner, Leipzig, 1986, 109-138.
  • [29] J. Santanilla, Existence of nonnegative solutions of a semilinear equations at resonance with linear growth, Proc. Amer. Math. Soc. 105 (1989), 963-971.
  • [30] M. Schechter, J. Shapiro and M. Snow, Solution of the nonlinear problem Au=Nu in a Banach space, Trans. Amer. Math. Soc. 241 (1978), 69-78.
  • [31] S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586.
  • [32] S. A. Williams, A connection between the Cesari and Leray-Schauder methods, Michigan Math. J. 15 (1968), 441-448.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv66i1p109bwm
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