科研之友
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摘要
We study elliptic Neumann problems in which the reaction term at infinity is resonant with respect to any pair {(lambda) over cap (m),(lambda) over cap (m)+1} of distinct consecutive eigenvalues. Using variational methods combined with Morse theoretic techniques, we show that when the double resonance occurs in a %26quot;nonprincipal%26quot; spectral interval [(lambda) over cap (m),(lambda) over cap (m)+1], m %26gt;= 1, we have at least three nontrivial smooth solutions, two of which have constant sign. If the double resonance occurs in the %26quot;principal%26quot; spectral [(lambda) over cap (0) = 0,(lambda) over cap (1)], then we show that the problem has at least one nontrivial smooth solution.
- 出版日期2012-3
