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Multiple Positive Solutions for a Class of Nonlinear Elliptic Eigenvalue Problems with a Sign-Changing Nonlinearity | | M. L. Carvalho
; J. V. Goncalves
; K. O. Silva
; | | Date: |
22 Oct 2013 | | Abstract: | In 2009 Loc and Schmitt established a result on sufficient conditions for
multiplicity of solutions of a class of nonlinear eignvalue problems for the
p-Laplace operator under Dirichlet boundary conditions, extending an earlier
result of 1981 by Peter Hess for the Laplacian. Results on necessary conditions
for existence were also established. In the present paper the authors extend
the main results by Loc and Schmitt to the $Phi$-Laplacian. To overcome the
difficulties with this much more general operator it was necessary to employ
regularity results by Lieberman, a strong maximum principle by Pucci and Serrin
and a general result on lower and upper solutions by Le. | | Source: | arXiv, 1310.5903 | | Services: | Forum | Review | PDF | Favorites | |
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