Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation

• Autorzy: Kajikiya R.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Emden-Fowler equation; sign-changing solution; positive solution; variational method; norm estimate

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 4
• Strony: 713--723
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kajikiya R.

• 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.