Positive solutions of singular problems with sign changing Carathéodory nonlinearities depending on x′

Journal of Mathematical Analysis and Applications

Volumn 279, Issue 2, 2003, Pages 597-616

  Agarwal, Ravi P ^a   O'Regan, Donal ^b   Staněk, Svatoslav ^c  

^a Florida Institute of Technology ^*  (United States)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

Borsuk antipodal theorem; Leray Schauder degree; Lower and upper function; Positive solution; Singular boundary value problem

Indexed keywords

EID: 0037507613     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00046-5     Document Type: Article

References (7)

1. R.P. Agarwal, D. O'Regan, V. Lakshmikantham, Existence criteria for singular boundary value problems modelling the membrane response of a spherical cap, Nonlinear Anal., to appear.
2. J. Baxley, A singular nonlinear boundary value problem: membrane response of a spherical cap, SIAM J. Appl. Math. 48 (1988) 497-505.
3. L.E. Bobisud, J.E. Calvert, W.D. Royalty, Some existence results for singular boundary value problems, Differential Integral Equations 6 (1993) 553-571.
4. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
5. D. O'Regan, Theory of Singular Boundary Value Problems, World Scientific, Singapore, 1994.
6. S. Staněk, On solvability of nonlinear boundary value problems for the equation (x′ + g(t,x,x′))′ = f(t,x,x′) with one-sided growth restriction on f, Arch. Math. (Brno) 38 (2002) 129-148.
7. M.X. Wang, A. Cabada, J.J. Nieto, Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions, Ann. Polon. Math. 58 (1993) 221-235.