Boundary value problems with solutions

• Autorzy: Herzog Gerd , Kunstmann Peer Chr.

Identyfikatory

DOI

10.7494/OpMath.2019.39.1.49

• Języki publikacji: EN

Abstrakty

EN

By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.

Słowa kluczowe

EN

Dirichlet boundary value problems solutions in convex sets; continuation method; ordered Banach spaces; concave solutions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 1
• Strony: 49--60
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Herzog Gerd

• Karlsruher Institut fur Technologie (KIT) Institut fur Analysis D-76128 Karlsruhe, Germany

autor

Kunstmann Peer Chr.

• Karlsruher Institut fur Technologie (KIT) Institut fur Analysis D-76128 Karlsruhe, Germany

Bibliografia

• [1] R.P. Agarwal, M. Meehan, D. O'Regan, Fixed point theory and applications, Cambridge Tracts in Mathematics, vol. 141, Cambridge University Press, Cambridge, 2001.
• [2] O. Alvarez, J.-M. Lasry, P.-L. Lions, Convex viscosity solutions and state constraints, J. Math. Pures Appl. 76 (1997), 265-288.
• [3] J. Appell, C.-J. Chen, S. Tseng, M. Vath, A continuation and existence result for a boundary value problem on an unbounded domain arising for the electrical potential in a cylindrical double layer, J. Math. Anal. Appl. 332 (2007), 1134-1147.
• [4] P.B. Bailey, L.F. Shampine, P.E. Waltman, Nonlinear two point boundary value problems, Mathematics in Science and Engineering, vol. 44, Academic Press, New York-London, 1968.
• [5] M. Frigon, A. Granas, Z.E.A. Guennoun, Alternative non lineaire pour les applications contractantes, Ann. Sci. Math. Quebec 19 (1995), 65-68.
• [6] A. Granas, Continuation method for contractive maps, Topol. Methods Nonlinear Anal. 3 (1994), 375-379.
• [7] P. Hartman, Ordinary differential equations, Classics in Applied Mathematics, 38. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002.
• [8] M. Keller-Ressel, E. Mayerhofer, A.G. Smirnov, On convexity of solutions of ordinary differential equations, J. Math. Anal. Appl. 368 (2010), 247-253.
• [9] R. Lemmert, P. Volkmann, Bnndwe.rtproble.me fur gewohnliche Differentialgleichungen in konvexen Teilmengen eines Banachraumes, J. Differential Equations 27 (1978), 138-143.
• [10] R. Lemmert, P. Volkmann, liber die Existenz von Losungen fur Randwertprobleme in konvexen Mengen, Arch. Math. 32 (1979), 68-74.
• [11] R. Lemmert, P. Volkmann, On the positivity of semigroups of operators, Commentat. Math. Univ. Carol. 39 (1998), 483-489.
• [12] R.H. Martin, Nonlinear operators and differential equations in Banach spaces, Pure and Applied Mathematics. Wiley-Interscience, New York-London-Sydney, 1976.
• [13] R. Redheffer, Matrix differential equations, Bull. Am. Math. Soc. 81 (1975), 485-488.
• [14] K. Schmitt, P. Volkmann, Boundary value problems for second order differential equations in convex subsets of a Banach space, Trans. Amer. Math. Soc. 218 (1976), 397-405.
• [15] P. Volkmann, Gewohnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorraumen, Math. Z. 127 (1972), 157-164.
• [16] P. Volkmann, liber die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume, Math. Ann. 203 (1973), 201-210.