Dimitrios A. Kandilakis
We study the following quasilinear problem with nonlinear boundary conditions
where is an unbounded domain in with a noncompact and smooth boundary , denotes the unit outward normal vector on , is the -Laplacian, , , and are nonnegative essentially bounded functions, and . The properties of the first eigenvalue and the associated eigenvectors of the related eigenvalue problem are examined. Then it is shown that if , the original problem admits an infinite number of solutions one of which is nonnegative, while if it admits at least one nonnegative solution. Our approach is variational in character.
Submitted September 27, 2004. Published May 31, 2005.
Math Subject Classifications: 35J20, 35J60.
Key Words: Variational method; fibering method; Palais-Smale condition; genus.
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| Dimitrios A. Kandilakis |
Department of Sciences
Technical University Of Crete
Chania, Crete, 73100 Greece
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