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On the solvability of semilinear differential equations at resonance

Published online by Cambridge University Press:  20 January 2009

Chung-Cheng Kuo
Chung-Cheng Kuo
Affiliation:
Department of Mathematics, Fu Jen University, Taipei, Taiwan, Republic of China
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Abstract

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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

Keywords

Landesman-Lazer conditionLeray-Schauder continuation method
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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