MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR THIRD-ORDER BOUNDARY VALUE PROBLEM IN ABSTRACT SPACES


Authors

FANG ZHANG - School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou, 213164, PR China.


Abstract

In this paper, we study the nonlinear singular boundary value problem in abstract spaces: \[ \begin{cases} u''' + f(t, u) = \theta,\,\,\,\,\, t \in (0, 1),\\ u(0) = u'(0) = \theta, u'(1) = \xi u'(\eta), \end{cases} \] where \(0 < \eta< 1\) and \(1 < \xi<\frac{1}{\eta}, \theta\) denotes the zero element of \(E, E\) is a real Banach space, and \(f(t, u)\) is allowed to be singular at both end point \(t = 0\) and \(t = 1\). We show the existence of at least two positive solutions of this problem.


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