Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T17:43:12.889Z Has data issue: false hasContentIssue false

Points of Spherical Maxima and Solvability of Semilinear Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

Martin Schechter
Affiliation:
University of California, Irvine, California 92717, U.S.A.
Kyril Tintarev
Affiliation:
University of California, Irvine, California 92717, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give mild sufficient conditions on a nonlinear functional to have eigenvalues. These results are intended for the study of boundary value problems for semilinear elliptic equations.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. De Figueiredo, D.G., Lions, P.-L., Nussbaum, R.D., A priori estimates and existence of positive solutions ofsemilinear elliptic equations, J. Math. Pures et Appl. 61(1982), 4163.Google Scholar
2. Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations. Conf. Board of Math. Sci., Reg. Conf. Ser. in Math., No. 65, Amer. Math. Soc, 1986.Google Scholar
3. Schechter, M., Spectra of partial differential operators. North Holland, 1986.Google Scholar
4. Schechter, M., Derivatives of mappings with applications to nonlinear differential equations, Trans. Amer. Math. Soc. 293(1986), 5369.Google Scholar
5. Schechter, M., Tintarev, K., Families of first eigenfunctions for semilinear elliptic eigenvalue problems,, Duke Math. J. 62(1991), 453465.Google Scholar
6. Schechter, M., Spherical maxima in Hilbert space and semilinear eigenvalue problems, Diff. Int. Eqns. (5)3 (1990), 889899.Google Scholar