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Points of Spherical Maxima and Solvability of Semilinear Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

Martin Schechter  and
Kyril Tintarev
Martin Schechter
Affiliation:
University of California, Irvine, California 92717, U.S.A.
Kyril Tintarev
Affiliation:
University of California, Irvine, California 92717, U.S.A.
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Abstract

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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.

Keywords

35P3035T6547H1247H15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 4 , 01 August 1991 , pp. 825 - 831
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), 41–63.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), 53–69.Google Scholar
5. Schechter, M., Tintarev, K., Families of first eigenfunctions for semilinear elliptic eigenvalue problems,, Duke Math. J. 62(1991), 453–465.Google Scholar
6. Schechter, M., Spherical maxima in Hilbert space and semilinear eigenvalue problems, Diff. Int. Eqns. (5)3 (1990), 889–899.Google Scholar