Applied Mathematics-A Journal of Chinese Universities

, Volume 21, Issue 2, pp 191-202

First online:

Research on the existence of solution of equation involving p-laplacian operator

  • Wei LiAffiliated withSchool of Mathematics and Statistics, Hebei University of Economics and BusinessInstitute of Applied Mathematics and Mechanics, Ordnance Engineering College
  • , Zhou HaiyunAffiliated withInstitute of Applied Mathematics and Mechanics, Ordnance Engineering College

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By using the perturbation theories on sums of ranges for nonlinear accretive mappings of Calvert and Gupta (1978), the abstract result on the existence of a solution u∈L p (Ω) to nonlinear equations involving p-Laplacian operator Δ p , where 2N/N+1<p<+∞ and N(≥1) denotes the dimension of R N , is studied. The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers. To obtain the result, some new techniques are used.

MR Subject Classification

47H05 47H09 49M05


maximal monotone operator accretive mapping hemi-continuous mapping p-Laplacian operator