Strong resonance problems for the one-dimensional p-Laplacian
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We study the existence of the weak solution of the nonlinear boundary-value problem
-(|u'|p-2u')' = λ|u|p-2u + g(u) - h(x) in (0, π),
u(0) = u(π) = 0,
where p and λ are real numbers, p > 1, h ∈ Lp' (0, π) (p' = p/p-1) and the nonlinearity g : ℝ → ℝ is a continuous function of the Landesman-Lazer type. Our sufficiency conditions generalize the results published previously about the solvability of this problem.
CitationBouchala, J. (2005). Strong resonance problems for the one-dimensional p-Laplacian. Electronic Journal of Differential Equations, 2005(08), pp. 1-10.
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