Research on the existence of solution of equation involving p -laplacian operator Authors Wei Li School of Mathematics and Statistics Hebei University of Economics and Business Institute of Applied Mathematics and Mechanics Ordnance Engineering College Zhou Haiyun Institute of Applied Mathematics and Mechanics Ordnance Engineering College Article

DOI :
10.1007/BF02791356

Cite this article as: Li, W. & Haiyun, Z. Appl. Math.- J. Chin. Univ. (2006) 21: 191. doi:10.1007/BF02791356
Abstract 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

Keywords maximal monotone operator accretive mapping hemi-continuous mapping p -Laplacian operatorSupported by the National Natural Science Foundation of China (10471033).

References 1.

Wei Li, He Zhen. The applications of sums of ranges of accretive operators to nonlinear equations involving the

p -Laplacian operator, Nonlinear Analysis, 1995, 24:185–193.

MATH CrossRef MathSciNet 2.

Wei Li. The existence of solution of nonlinear elliptic boundary value problem, Mathematics in Practice and Theory, 2001, 31:360–364.

3.

Wei Li, He Zhen. The applications of theories of accretive operators to nonlinear elliplic boundary valuc problems in

L
^{p} -spaces, Nonlinear Analysis, 2001, 46:199–211.

MATH CrossRef MathSciNet 4.

Wei Li, Zhou Haiyun. Existence of solutions of a family of nonlinear bundary value problems in

L
^{2} -spaces, Appl Math J Chinese Univ Ser B, 2005, 20:175–182.

MATH CrossRef MathSciNet 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.

6.

Li Likang, Gou Yutao. The Theory of Sobolev Space (in Chinese), Shanghai: Shanghai Science and Technology Press, 1981, 120–142.

7.

Calvert B D, Gupta C P. Nonlinear elliplic boundary value problems in

L
^{p} -spaces and sums of ranges of accretive operators, Nonlinear Analysis, 1978, 2:1–26.

MATH CrossRef MathSciNet 8.

Wang Yaodong, The Theories of Partial Differential Equations in L
^{2} Space, Beijing: Beijing University Press (in Chinese), 1989.

9.

Brezis H. Integrales convexes dans les espaces de Sobolev, Israel J Math, 1972, 13:1–23.

CrossRef MathSciNet © Editorial Committee of Applied Mathematics-A Journal of Chinese Universities 2006