Multiple solutions for an asymptotically linear Duffing equation with Neumann boundary value conditions. (English) Zbl 1228.34034
Using index theory for linear Duffing equations and Morse theory, the authors obtain multiplicity results for the Neumann boundary value
\[ x'' + f(t,x) = 0, \quad x'(0) = 0 = x'(1), \]
where \(f\) is of class \(C^1\) and has linear growth. Depending upon the assumptions, they obtain the existence of at least one or at least two solutions.
\[ x'' + f(t,x) = 0, \quad x'(0) = 0 = x'(1), \]
where \(f\) is of class \(C^1\) and has linear growth. Depending upon the assumptions, they obtain the existence of at least one or at least two solutions.
Reviewer: Jean Mawhin (Louvain-La-Neuve)
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
Duffing equation; resonance; multiple solutions; Neumann problem; index theory; Morse theoryReferences:
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