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Języki publikacji
Abstrakty
We study the sublinear Emden-Fowler equation in small domains. As the domain becomes smaller, so does any solution. We investigate the convergence rate of the Sobolev norm of solutions as the volume of the domain converges to zero. The result is obtained by estimating the first eigenvalue of the Laplacian with the help of the variational method.
Czasopismo
Rocznik
Tom
Strony
713--723
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Saga University Faculty of Science and Engineering Department of Mathematics Saga, 840-8502, Japan
Bibliografia
- [1] A. Ambrosetti, M. Badiale, The dual variational principle and elliptic problems with discontinuous nonlinearities, J. Math. Anal. Appl. 140 (1989), 363–373.
- [2] A. Ambrosetti, H. Brezis, G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), 519–543.
- [3] H. Brezis, L. Oswald, Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986), 55–64.
- [4] I. Chavel, Eigenvalues in Riemannian geometry, Pure and Applied Mathematics, vol. 115, Academic Press, New York, 1984.
- [5] R. Kajikiya, Comparison theorem and uniqueness of positive solutions for sublinear elliptic equations, Archiv der Mathematik 91 (2008), 427–435.
- [6] R. Kajikiya, A priori estimates of positive solutions for sublinear elliptic equations, Trans. Amer. Math. Soc. 361 (2009), 3793–3815.
- [7] R. Kajikiya, Non-radial least energy solutions of the generalized Hénon equation, J. Differential Equations 252 (2012), 1987–2003.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a78022f1-323c-4227-8fa6-7cbe73901018