Existence results for asymptotic linear Hammerstain integral equations via Morse Theory

• Autorzy: O'Regan D.
• Języki publikacji: EN

Abstrakty

EN

In this paper we establish some results for asymptotic linear Hammerstein integral equations. Using Morse theory and in particular critical groups we prove a number of existence results.

Słowa kluczowe

EN

asymptotic linear; critical groups; existence

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2009
• Tom: Vol. 49, [Z] 1
• Strony: 59--66
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

O'Regan D.

• Department Of Mathematics, National University of Ireland Galway, Ireland,

Bibliografia

• [1] R.P. Agarwal, K. Perera and D. O'Regan, Multiplicity results for p-sublinear p-Laplacian problems involving indfinite eigenvalue problems via Morse theory, to appear.
• [2] K.C. Chang, Ifinite-dimensional Morse theory and multiple solution problems, Progress in Nonlinear Differential Equations and their Applications, Vol. 6, Birkhäuser, Boston, 1993.
• [3] M.A. Krasnoselskii, Topological methods in the theory of nonlinear integral equations, Perga-mon, Oxford, 1964.
• [4] F. Li, Y. Li and Z. Liang, Existence of solutions to nonlinear Hammerstein integral equations and applications, Jour. Math. Anal. Appl. 323 (2006), 209{227.
• [5] J.Q. Liu and S.H. Li, An existence theorem for multiple critical points and its application, Kexue Tongbao (Chinese) 29 (1984), 1025{1027.
• [6] D. O'Regan, Multiplicity results for sublinear and superlinear Hammerstein integral equations via Morse theory, Communications in Applied Analysis, to appear.
• [7] K. Perera, R.P. Agarwal and D. O'Regan, Morse-theoretic aspects of p-Laplacian type operators, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, Boston, to appear.
• [8] R. Precup, Methods in nonlinear integral equations, Kluwer, Dordrecht, 2002.
• [9] N. Young, An introduction to Hilbert spaces, Cambridge University Press, Cambridge, 1989.