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On the solvability of semilinear differential equations at resonance
Published online by Cambridge University Press: 20 January 2009
Abstract
In this paper we use the Leray–Schauder continuation method to study the existence of solutions for semilinear differential equations Lu + g(x, u) = h, in which the linear operator L on L2(Ω) may be non-self-adjoint, the L2(Ω)-function h belongs to N⊥(L), the nonlinear term g(x, u) ∈ O(|u|α) as |u| → ∞ for some 0 ≤ α < 1 and satisfies
for all v ∈ N(L) – {0}, where and
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 1 , February 2000 , pp. 103 - 112
- Copyright
- Copyright © Edinburgh Mathematical Society 2000
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