Sublinear Elliptic Equation on Fractal Domains
Sublinear Elliptic Equation on Fractal Domains
摘要
This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a（x）｜u｜q-1u-f（x,u）,with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.
参考文献11
-
1Kigami J., Analysis on Fractals. Cambridge University Press, 2004.
-
2Kigami J., Harmonic calculus on p.c.f self-similar sets. Trans. Amer. Math. Soc., 335 (1993), 721-755.
-
3Falconer J. K., Semi-linear PDES on self-similar fractals. Commun. Math. Phys., 206 (1999), 235-245.
-
4Fukushima M. and Shima T., On a spectral analysis for the Sierpinski gasket. Potential Anal., 1 (1992), 1-35.
-
5Falconer J. K. and Hu J., Non-linear elliptic equations on the Sierpinski gasket. J. Math. Anal. Appl., 240 (1999), 552-573.
-
6Chen H. and He Z. Y., Semi-linear elliptic equations on fractal sets. Acta Math. Sci., 29 (2009), 222-242.
-
7Chang K.-C., Critical Theory and Its Applications. (in chinese). Shanghai Science and Tech- nology Press, 1986.
-
8Rabinowitz P. H., Minimax Methods in Critical Point Theory with Applications to Differential Equations. Expository Lectures form CBMS Regional Conference held at University of Miami, Amer. Math. Soc., Providence, RI, 1986.
-
9Strichartz R. S., Some properties of Laplacian on fractals. J. Func. Anal., 164 (1999), 181-208.
-
10Kolzov S. M., Harmonization and homogenization on fractals. Commun. Math. Phys., 153 (1993), 339-357.
-
1Ximo GUAL-ARNAU,Antonio M.NAVEIRA.Volume of Domains in Symmetric Spaces[J].Chinese Annals of Mathematics,Series B,2007,28(5):521-526.
-
2HASSIB Moulay Cherif,AKDIM Youssef,AZROUL Elhoussine,BARBARA Abdelkrim.Existence and Regularity of Solution for Strongly Nonlinear p（x）-Elliptic Equation with Measure Data[J].Journal of Partial Differential Equations,2017,30(1):31-46.
-
3WEI Zhongli(Department of Fundamental Courses, Shandong Arehitectuml andCivil Engineering Institute, Ji’nan 250014, China).POSITIVE SOLUTIONS OF SINGULAR SUBLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS[J].Systems Science and Mathematical Sciences,1998,11(1):82-88. 被引量：12
-
4PENG Yu-cheng,SHI Dong-yang.A New Proof of Superclose of a Crouzeix-Raviart Type Finite Element for Second Order Elliptic Equation[J].Chinese Quarterly Journal of Mathematics,2007,22(4):627-632.
-
5曹丽.SOME ASYMPTOTIC PROPERTIES OF THE CONVOLUTION TRANSFORMS OF FRACTAL MEASURES[J].Acta Mathematica Scientia,2012,32(6):2096-2104.
-
6YANG HAITAO AND WU SHAOPING.ON SEMILINEAR ELLIPTIC EQUATIONS WITH SUBLINEAR AND SUPERLINEAR NONLINEARITIES IN R^N[J].Applied Mathematics(A Journal of Chinese Universities),1997,12(1):69-78.
-
7吴敏.HAUSDORFF DIMENSION OF CUTSET OF COMPLEX VALUED RADEMACHER SERIES[J].Acta Mathematicae Applicatae Sinica,2000,16(2):140-148. 被引量：1
-
8HE Zhenya CHEN Hua.Non-Linear Elliptic Equations on Fractal Domain[J].Wuhan University Journal of Natural Sciences,2007,12(3):391-394.
-
9曹道珉.MULTIPLE POSITIVE SOLUTIONS OF INHOMOGENEOUS SEMILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS IN R^2[J].Acta Mathematica Scientia,1994,14(3):297-312. 被引量：1
-
10田立新,刘玉荣,刘曾荣.LOCAL ATTRACTORS FOR WEAKLY DAMPED FORCED KdV EQUATION IN THIN 2D DOMAINS[J].Applied Mathematics and Mechanics(English Edition),2000,21(10):1131-1138.
