POSITIVE SOLUTIONS FOR NONLINEAR SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS WITH SIGN CHANGING NONLINEARITIES
Abstract
In this paper, we investigate nonlinear second-order m-point boundary value problem
u''(t) + \lambda h(t) f(t, u) = 0, 0 < t < 1,
\beta u(0) - \gamma u'(0) = 0, u(1) = \sum_{i=1}^{m-2} \alpha_i u(\xi_i),
where the nonlinear term f is allowed to change sign. The existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree. Moreover, the associated Green's function for the above problem is also given.
u''(t) + \lambda h(t) f(t, u) = 0, 0 < t < 1,
\beta u(0) - \gamma u'(0) = 0, u(1) = \sum_{i=1}^{m-2} \alpha_i u(\xi_i),
where the nonlinear term f is allowed to change sign. The existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree. Moreover, the associated Green's function for the above problem is also given.
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