Research on the existence of solution of equation involving p-laplacian operator
- 30 Downloads
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∈Lp(Ω) to nonlinear equations involving p-Laplacian operator Δp, where 2N/N+1<p<+∞ and N(≥1) denotes the dimension of RN, 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 Classification47H05 47H09 49M05
Keywordsmaximal monotone operator accretive mapping hemi-continuous mapping p-Laplacian operator
Unable to display preview. Download preview PDF.
- 2.Wei Li. The existence of solution of nonlinear elliptic boundary value problem, Mathematics in Practice and Theory, 2001, 31:360–364.Google Scholar
- 5.Wei Li, Zhou Haiyun. The existence of solution of nonlinear elliptic boundary value problem in L p-spaces, Mathematics in Practice and Theory, 2005, 35:160–167.Google Scholar
- 6.Li Likang, Gou Yutao. The Theory of Sobolev Space (in Chinese), Shanghai: Shanghai Science and Technology Press, 1981, 120–142.Google Scholar
- 8.Wang Yaodong, The Theories of Partial Differential Equations in L 2 Space, Beijing: Beijing University Press (in Chinese), 1989.Google Scholar