PARAMETERIZED NONLINEAR EQUATIONS ON DIRICHLET FORMS

TitlePARAMETERIZED NONLINEAR EQUATIONS ON DIRICHLET FORMS
Publication TypeJournal Article
Year of Publication2009
AuthorsKRISTÀLY, ALEXANDRU, O’REGAN, DONAL, VARGA, CSABA
Volume13
Issue3
Start Page317
Pagination9
Date Published2009
ISSN1083-2564
AMS31C25, 35B38
Abstract

By using variational techniques we prove the existence of two nontrivial solutions for a parameterized nonlinear equation relative to Dirichlet forms.

URLhttp://www.acadsol.eu/en/articles/13/3/4.pdf
Refereed DesignationRefereed
Full Text

REFERENCES
[1] M. Biroli, S. Mataloni, M. Matzeu, Stability results for Mountain Pass and linking type solutions
of semilinear problems involving Dirichlet forms. NoDEA: Nonlinear Differential Equations
and Applications 12 (2005), 295–321.
[2] M. Biroli, S. Tersian, On the existence of nontrivial solutions to a semilinear equation relative
to a Dirichlet form. Rendiconti Istituto Lombardo (Rend.Sc.) A 131 (1998), 151–168.
[3] K. J. Falconer, Semilinear partial differential equations on self-similar fractals. Comm. Math.
Phys. 206 (1999), 235–245.
[4] K. J. Falconer, J. Hu, Nonlinear elliptical equations on the Sierpinski gasket. J. Math. Anal.
Appl. 240 (1999), 552–573.
[5] K. J. Falconer, J. Hu, Nonlinear diffusion equations on unbounded fractal domains. J. Math.
Anal. Appl. 256 (2001), 606–624.
[6] M. Fukushima, Dirichlet forms, diffusion processes and spectral dimensions for nested fractals.
In : Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988),
151–161. Cambridge University Press: Cambridge, 1992.
[7] A. Grigor’yan, J. Hu, K.-S. Lau, Heat kernels on metric measure spaces and an application to
semilinear elliptic equations. Trans. Am. Math. Soc. 355 (2003), 2065–2095.
[8] J. Hu, Multiple solutions for a class of nonlinear elliptic equations on the Sierpin’ski gasket.
Sci. China Ser. A 47 (2004), no. 5, 772–786.
[9] S. Kusuoka, Z. X. Yin, Dirichlet forms on fractals: Poincar´e constant and resistance. Probability
Theory and Related Fields, 93 169–196, 1992.
[10] H. Lisei, Cs. Varga, Multiple solutions for nonlinear equations involving Dirichlet forms. Topics
in mathematics, computer science and philosophy, 135–145, Presa Univ. Clujeana (ClujNapoca),
2008.
[11] M. Matzeu, Mountain Pass and Linking Type Solutions for Semilinear Dirichlet Forms. Progr.
in Non. Diff. Eq. and Appl. 40 (2000), 217–231.