JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (08): 72-77.doi: 10.6040/j.issn.1671-9352.0.2014.485

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Existence of solutions for singular φ-Laplacian of periodic boundary value problems

XU Man   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2014-11-04 Online:2015-08-20 Published:2015-07-31

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Abstract: We consider the existence of solutions for singular φ-Laplacian of periodic boundary value problems
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where φ:(-a,a)→R(0< a <+∞) is an increasing homeomorphism such that φ(0)=0, g∈ C(R,R), e∈C[0,T], and s is a parameter. The proof of the main result is based on the continuation theorem and Leray-Schauder degree arguments.

Key words: periodic boundary value problems, continuation theorem, Leray-Schauder degree, φ-Laplacian

CLC Number: 

  • O175.8
[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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