An approach to nonlinear elliptic boundary value problems
1983 ◽
Vol 34
(3)
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pp. 316-335
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Keyword(s):
AbstractLet D ⊂ Rn be a bounded domain and L: dom L ⊂ L2 (D) → L2 (D) be a self-adjoint operator of finite dimensional kernel. Let f: D × R → R be a function satisfying the Carathéodory condition. Assume that there are constants λ > 0 and δ ∈ [0, 1] such that and that .Then with the aid of a generalized Krasnosel'skii's theorem it has been proved that under conditions exactly analogous to those of Landesman and Lazer there exists u ∈ L2(D) such that L(u)(x) = f(x, u(x)) for ∀x ∈ D. This result is then used to prove the existence of weak solutions of nonlinesr elliptic boundary value problems.Other abstract results applicable to ordinary and partial differential equations have also been proved.
2015 ◽
Vol 17
(1)
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pp. 43-64
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1992 ◽
Vol 115
(4)
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pp. 1031-1031
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1974 ◽
Vol 190
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pp. 163-163
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1974 ◽
pp. 235-247
1996 ◽
Vol 19
(2)
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pp. 387-396
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2011 ◽
Vol 284
(14-15)
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pp. 1872-1879
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