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Structure of nonnegative nontrivial and positive solutions of singularly perturbedp-laplace equations

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Abstract

Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

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Authors and Affiliations

  1. College of Sciences, Xi’an Jiaotong University, 710049, Xi’an, P. R. China

    Zhang Zheng-ce Lecturer, Doctor & Li Kai-tai

Authors
  1. Zhang Zheng-ce Lecturer, Doctor
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  2. Li Kai-tai
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Additional information

Communicated by LIN Zong-chi, Original Member of Editorial Committee, AMM

Foundation items: the National Key Basic Research Development Project Program of China (1999032801); the National Natural Science Foundation of China (10371095)

Biography: ZHANG Zheng-ce (1976≈)

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Zheng-ce, Z., Kai-tai, L. Structure of nonnegative nontrivial and positive solutions of singularly perturbedp-laplace equations. Appl Math Mech 25, 929–936 (2004). https://doi.org/10.1007/BF02438801

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  • DOI: https://doi.org/10.1007/BF02438801

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Chinese Library Classification

2000 Mathematics Subject Classification

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