Existence Results for Some Fourth Order Boundary Value Problems With a Parameter
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摘要: 延续Yang和Zhang的工作,研究了带有参数的某四阶边值问题非平凡解的存在性.对于此边值问题的非线性项,不改变其在无穷远处的条件,只是改变了在零点处的条件,综合利用临界点理论,收缩性质及流不变集理论,得到了正解、 负解及变号解的存在性.Abstract: A sequel to Yang, Zhang [Nonlinear Anal, 2008, 69:1364-1375.] in which nontrivial solutions for the fourth order boundary value problems are studied. Now under the same conditions near in finity, but different from the conditions near zero, positive, negative, and sign-changing solutions are obtained by combining critical point theory, retracting property and invariant sets.
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Key words:
- boundary value problem /
- critical point /
- invariant sets /
- retracting property
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