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YAO Qing-liu. Existence theorem of positive solution to a nonlinear Sturm-Liouville problem (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2009, (1): 32-36.
Citation:
YAO Qing-liu. Existence theorem of positive solution to a nonlinear Sturm-Liouville problem (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2009, (1): 32-36.
YAO Qing-liu. Existence theorem of positive solution to a nonlinear Sturm-Liouville problem (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2009, (1): 32-36.
Citation:
YAO Qing-liu. Existence theorem of positive solution to a nonlinear Sturm-Liouville problem (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2009, (1): 32-36.
The existence of positive solution was studied for thenonlinear Sturm-Liouville boundary value problem, where thenonlinear term $f(t,u)$ may be singular at $t = 0,\,t = 1$. Byintroducing the integrations of height functions of nonlinear termon bounded set the growths of nonlinear term were described. Byapplying the Krasnoselskii fixed point theorem in degree theory andthe dominated convergence theorems in real variable, an existencetheorem of positive solution was proved when there are limitfunctions $\mathop {\lim }\limits_{u \to + 0} f(t,u) / u$ and$\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$.
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