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Resonance and Nonresonance in Terms of Average Values

✍ Scribed by M.N. Nkashama; S.B. Robinson

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
678 KB
Volume
132
Category
Article
ISSN
0022-0396

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✦ Synopsis

We prove existence results for nonlinear two-point boundary value problems. What sets our results apart is that we impose sufficient conditions for solvability in terms of the (asymptotic) average values of the nonlinearities. Our solvability conditions allow the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense.

1996 Academic Press, Inc.

where k is a positive integer, g : R Γ„ R is a continuous function with at most linear growth, and h # L 2 [0, ?]. What sets our results apart is that we impose sufficient conditions for solvability in terms of the average values of g(t) and g(t)Γ‚t for large |t|. For example, consider the result in , where article no.

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