Positive solutions of a non-linear eigenvalue problem with discontinuous non-linearity
1979 ◽
Vol 83
(1-2)
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pp. 133-145
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Keyword(s):
SynopsisWe seek non-trivial solutions (u,λ)∈C1([0,1])×[0,∞ with u(x)≧0 for all x ∈[0,1], of the nonlinear eigenvalue problem –u″(x)=λf(u(x)) for x ∈ (0,1) and u(0)=u(1)=0,where f:[0,∞)→[0,∞) is such that f(p) = 0, for p ∈ [0,1), and f(p) = K(p), for p ∈ (1,∞), and K: [1, ∞)→(0, ∞) is assumed to be twice continuously differentiable. (The value ƒ(1) is only required to be positive.)Existence and multiplicity theorems are given in the cases where ƒ is asymptotically sub-linear and ƒ is asymptotically super-linear. Moreover if strengthened assumptions are made on the growth of the non-linear term ƒ we obtain the precise number of non-trivial solutions for given values of λ ∈ [0, ∞).
2004 ◽
Vol 132
(6)
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pp. 1721-1728
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2009 ◽
Vol 215
(3)
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pp. 1077-1083
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2001 ◽
Vol 52
(3)
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pp. 433-447
Keyword(s):
2011 ◽
Vol 27
(3)
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pp. 367-372
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2014 ◽
Vol 21
(1)
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pp. 179-184
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Keyword(s):
2011 ◽
Vol 50-51
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pp. 185-189
2017 ◽
Vol 147
(4)
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pp. 875-894
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2020 ◽
Vol 21
(01)
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pp. 18-22
Keyword(s):
2001 ◽
Vol 261
(1)
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pp. 192-204
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