山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (08): 72-77.doi: 10.6040/j.issn.1671-9352.0.2014.485
徐嫚
XU Man
摘要： 考虑了奇异 φ-Laplacian 周期边值问题
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解的存在性, 其中 φ:(-a, a)→R是单调递增的同胚且 φ(0)=0, 0< a <+∞, g∈ C(R,R), e∈C[0,T], s 是一个参数.主要结果的证明基于紧集连通理论及Leray-Schauder度理论.
中图分类号:
| [1] BEREANU C, GHEORGHE D, ZAMORA M. Non-resonant boundary value problems with singular φ-Laplacian operators[J]. Nonlinear Differential Equations and Applications, 2013, 20(3):1365-1377. [2] MACCOLL L A. Theory of the relativistic oscillator[J]. American Journal of Physics, 1957, 25(8):535-538. [3] GRENIER W. Classical mechanics-point particles and relativity[M]. Berlin: Springer, 2004. [4] BEREANU C, MAWHIN J. Periodic solutions of nonlinear perturbations of φ-Laplacians with possibly bounded φ[J]. Nonlinear Analysis, 2008, 68(2):1668-1681. [5] BEREANU C, MAWHIN J. Existence and multiplicity results for some nonlinear problems with singular φ-Laplacian[J]. Journal of Differential Equations, 2007, 243(2):536-557. [6] BEREANU C, MAWHIN J. Boundary-value problems with non-surjective φ-Laplacian and one-sided bounded nonlinearity[J]. Advance in Differential Equations, 2006, 11(1):35-60. [7] LAZER A C, SOLIMINI S. On periodic solutions of nonlinear differential equations with singularities[J]. Proceedings of the American Mathematical Society, 1987, 99(1):109-114. [8] MANÁSEVICH R, MAWHIN J. Boundary value problems for nonlinear peturbations of vector p-Laplacian-like operators[J]. Journal of Korean Mathmatical Society, 2000, 37:665-685. [9] BEREANU C, MAWHIN J. Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and -Laplacian[J]. Nonlinear Differential Equations and Applications, 2008, 15(1-2):159-168. [10] BEREANU C, GHEORGHE D, ZAMORA M. Periodic solutions for singular perturbations of the singular φ-Laplacian operator[J]. Communications in Contemporary Mathematics, 2013, 15(4):1-22. [11] MAWHIN J, REBELLO C, ZANOLIN F. Continuation throrems for Ambrosetti-Prodi type periodic problems[J]. Communications in Contemporary Mathematics, 2000, 2(1):87-126. [12] MASSABÓ I, PEJSACHOWICZ J. On the connectivity properties of the solution set of parametrized families of compact vector fields[J]. Journal of Functional Analysis, 1984, 59(2):151-166. |
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