Potential Landesman-Lazer type conditions and the Fucik spectrum
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We prove the existence of solutions to the nonlinear problem
u''(x) + λ+u+(x) = λ_u-(x) + g(x, u(x)) = ƒ(x), x ∈ (0, π),
u(0) = u(π) = 0
where the point [λ+, λ_] is a point of the Fučík spectrum and the nonlinearity g(x, u(x)) satisfies a potential Landesman-Lazer type condition. We use a variational method based on the organization of the Saddle Point Theorem.
CitationTomiczek, P. (2005). Potential Landesman-Lazer type conditions and the Fučík spectrum. Electronic Journal of Differential Equations, 2005(94), pp. 1-12.
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