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1997 | 17 | 1-2 | 67-81
Tytuł artykułu

Periodic solutions for quasilinear vector differential equations with maximal monotone terms

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.
Twórcy
  • National Technical University, Department of Mathematics, Zografou Campus Athens 157 80, Greece
  • National Technical University, Department of Mathematics, Zografou Campus Athens 157 80, Greece
Bibliografia
  • [1] R. Ash, Real Analysis and Probability, Academic Press, New York 1972.
  • [2] L. Boccardo, P. Drabek, D. Giachetti, and M. Kuera, Generalization of Fredholm alternative for nonlinear differential operators, Nonl. Analysis, Theory, Math., Appl. 10 (1986), 1083-1103.
  • [3] A. Cabada and J. Nieto, Extremal solutions for second order nonlinear periodic boundary value problems Appl. Math. Comp. 40 (1990), 135-145.
  • [4] W. Gao and J. Wang, On a nonlinear second order periodic boundary value problem with Carathéodory functions, Ann. Polon. Math. 62 (1995), 283-291.
  • [5] Z. Guo, Boundary value problems of a class of quasilinear ordinary differential equations Diff. Integral Equations 6 (1993), 705-719.
  • [6] H.W. Knobloch, On the existence of periodic solutions for second order vector differential equations J. Diff. Equations 9 (1971), 67-85.
  • [7] J. Nieto, Nonlinear second-order periodic boundary value problens J. Math. Anal. Appl. 130 (1988), 22-29.
  • [8] P. Omari, and M. Trombetta, Remarks on the lower and upper solutions method for second and third order periodic boundary value problems Appl. Math. Comp. 50 (1992), 1-21.
  • [9] M.P. Pino, M. Elgueta and Manasevich, A homotopic deformation along p of a Leray-Schauder degree result and existence for (|u'|^{p-2}u')'+f(t,u) = 0,u(0) = u(T) = 0,p > 1, J. Diff. Equations 80 (1989), 1-13.
  • [10] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-div17i1-2n5bwm
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