Existence of solutions to a class of nonlinear second order two-point boundary value problems |
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| Authors: | Fuyi Li Zhanping Liang Qi Zhang |
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| Affiliation: | a Department of Mathematics, Shanxi University, Taiyuan 030006, People's Republic of China
b Department of Mathematics, Xinzhou Teachers' University, Xinzhou 034000, Shanxi, People's Republic of China |
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| Abstract: | In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem −u″(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u′(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role. |
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| Keywords: | Two-point boundary value problem Strongly monotone operator principle Critical point theory P.S. condition Mountain pass lemma |
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