Countably many solutions of a fourth order boundary value problem

N. Kosmatov, Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, USA

E. J. Qualitative Theory of Diff. Equ., No. 12. (2004), pp. 1-15.

Abstract: We apply fixed point theorems to obtain sufficient conditions for existence of infinitely many solutions of a nonlinear fourth order boundary value problem
$$\displaylines{ u^{(4)}(t) = a(t)f(u(t)), \quad 0 < t < 1, \cr u(0) = u(1) = u'(0) = u'(1) = 0, }$$
where $a(t)$ is $L^p$-integrable and $f$ satisfies certain growth conditions.

You can download the full text of this paper in DVI, PostScript or PDF format.