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- W2346187465 abstract "This paper is concerned with the solvability of the system−Δu−ν1θ1v=f(x,u,v)+h1(x) in Ω;−Δv−ν1θ2u=g(x,u,v)+h2(x) in Ω;u=v=0 on ∂Ω, at resonance at the simple eigenvalue ν1 of the corresponding linear eigenvalue problem. Here Ω⊂RN (N≥1) is a bounded domain with C2,η-boundary ∂Ω, η∈(0,1) (a bounded interval if N=1) and θ1, θ2 are positive constants. The nonlinear perturbations f(x,u,v),g(x,u,v):Ω×R2→R are Carathéodory functions that are sublinear at infinity. We employ the Lyapunov–Schmidt method to provide sufficient conditions on h1,h2∈Lr(Ω); r>N, to guarantee the solvability of the system." @default.
- W2346187465 created "2016-06-24" @default.
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- W2346187465 date "2016-10-01" @default.
- W2346187465 modified "2023-09-28" @default.
- W2346187465 title "On the solvability of asymptotically linear systems at resonance" @default.
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- W2346187465 doi "https://doi.org/10.1016/j.jmaa.2016.04.066" @default.
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