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## Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2001 | 21 | 1 | 127-148
Tytuł artykułu

### Nonlinear multivalued boundary value problems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $domA ≠ ℝ^{N}$ and $domA = ℝ^{N}$, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
127-148
Opis fizyczny
Daty
wydano
2001
otrzymano
2000-07-10
Twórcy
autor
• Center of Mathematics, Technical University Muenchen, Arcisstr. 21, D-80333 Muenchen, Germany
• National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
Bibliografia
• [1] R. Bader, A topological fixed point theory for evolution inclusions, submitted.
• [2] R. Bader and N.S. Papageorgiou, Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions, Annales Polonici Math. LXIII (2000), 69-93.
• [3] L. Boccardo, P. Drabek, D. Giachetti and M. Kucera, Generalization of Fredholm alternative for nonlinear differential operators, Nonlinear Anal. 10 (1986), 1083-1103.
• [4] H. Dang and S.F. Oppenheimer, Existence and uniqueness results for some nonlinear boundary value problems, J. Math. Anal. Appl. 198 (1996), 35-48.
• [5] M. Del Pino, M. Elgueta and R. 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, J. Diff. Eqns 80 (1989), 1-13.
• [6] M. Del Pino, R. Manasevich and A. Murua, Existence and multiplicity of solutions with prescribed period for a second order quasilinear o.d.e., Nonlinear Anal. 18 (1992), 79-92.
• [7] L. Erbe and W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y(t),y'(t)), Annales Polonici Math. 54 (1991), 195-226.
• [8] C. Fabry and D. Fayyad, Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities, Rend. Istit. Mat. Univ. Trieste 24 (1992), 207-227.
• [9] M. Frigon, Theoremes d'existence des solutions d'inclusions differentielles, NATO ASI Series, section C, vol. 472, Kluwer, Dordrecht, The Netherlands (1995), 51-87.
• [10] Z. Guo, Boundary value problems of a class of quasilinear ordinary differential equations, Diff. Integral Eqns 6 (1993), 705-719.
• [11] N. Halidias and N.S. Papageorgiou, Existence and relaxation results for nonlinear second order multivalued boundary value problems in $ℝ^N$, J. Diff. Eqns 147 (1998), 123-154.
• [12] P. Hartman, Ordinary Differential Equations, J. Wiley, New York 1964.
• [13] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands 1997.
• [14] D. Kandilakis and N.S. Papageorgiou, Existence theorems for nonlinear boundary value problems for second order differential inclusions, J. Diff. Eqns 132 (1996), 107-125.
• [15] R. Manasevich and J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Diff. Eqns 145 (1998), 367-393.
• [16] M. Marcus and V. Mizel, Absolute continuity on tracks and mappings of Sobolev spaces , Arch. Rational Mech. Anal. 45 (1972), 294-320.
• [17] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990.
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Bibliografia
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