STRONG RESONANCE PROBLEMS FOR THE ONE-DIMENSIONAL p-LAPLACIAN
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چکیده
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.
منابع مشابه
RESONANCE PROBLEMS FOR THE ONE-DIMENSIONAL p-LAPLACIAN
We consider resonance problems for the one dimensional p-Laplacian, and prove the existence of solutions assuming a standard LandesmanLazer condition. Our proofs use variational techniques to characterize the eigenvalues, and then to establish the solvability of the given boundary value problem.
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تاریخ انتشار 2005