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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:

2010年03期

Page:

14-18

Research Field:

数学

Publishing date:

Info

Title:

Infinitely Many Solutions for a Superlinear p-Laplacian Equation With Hardy Potential

Author(s):

Yu Boqiang¹; ²; Yao Yangxin¹; Zheng Qiufang¹; Shen Hui¹

1.Department of Mathematics,School of Science,South China University of Technology,Guangzhou 510640,China 2. Guangzhou C ity C ons truct ion College, Guangzhou 510900, Ch ina

Keywords:

H ardy. s inequa lity;  infin itely many so lutions;  Ce ram i. s condition;  Founta in theorem

PACS:

O175.25

DOI:

-

Abstract:

Th is paper considers a supe rlinear p-Laplac ian equation w ith H ardy po ten tia.l Thanks to H ardy. s inequa lity, infinite ly m any solutions are obtained through the Founta in theo rem w ith Ceram i. s cond ition

References:

[ 1] Ga rc ia Azorero J, Pe ra l A lonso I. Ex istence and nonunqueness for the p-Laplac ian[ J]. Nonlinear e igenva lues Communications in P. D. E, 1987, 12( 12): 1 389-1 430.
[ 2] Garc ia A zorero J, Pera lA lonso I. M ultip lic ity of so lutions fo r e lliptic problem s w ith c ritica l exponent o rw ith a nonsymme tric term [ J]. Transac tions of the Ame ricanM athem atica l Soc ie ty, 1991, 323( 2): 877-895.
[ 3] Ub illa P. Mu ltiplicity resu lts fo r the 1-D im ensiona l gene ra lized p-Laplacian[ J] . JM ath Ana l App,l 1995, 190( 2 ): 611- 623.
[ 4] Caffare lli L, Kohn R, N irenberg L. F irst o rder interpo lation inequality w ith w e ights[ J]. CompusM a th, 1984( 53 ): 259- 275.
[ 5] Bartsch T. Infin itym any so lutions o f a symm etr ic Dir ichlet prob lem [ J]. Nonl Ana l TMA, 1993, 20: 1 205-1 216.
[ 6] Yang H, Fan X L. Ex isitence o f infin ity m any solutions o f the p-Laplace equation w ith p-concave and convex nonlinearities [ J] . J Lanzhou Univ Nat Sc,i 1992, 35( 2): 12-16.

Memo

Memo:

-

Common functions

Last Update: 2013-04-08