Resonance problems for the one-dimensional $p$-Laplacian
نویسندگان
چکیده
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.
متن کاملSTRONG RESONANCE PROBLEMS FOR THE ONE-DIMENSIONAL p-LAPLACIAN
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...
متن کاملLOWER BOUNDS FOR EIGENVALUES OF THE ONE-DIMENSIONAL p-LAPLACIAN
We also prove that the lower bound is sharp. Eigenvalue problems for quasilinear operators of p-Laplace type like (1.1) have received considerable attention in the last years (see, e.g., [1, 2, 3, 5, 8, 13]). The asymptotic behavior of eigenvalues was obtained in [6, 7]. Lyapunov inequalities have proved to be useful tools in the study of qualitative nature of solutions of ordinary linear diffe...
متن کاملA Note on Strong Resonance Problems for P-laplacian
In this note, we study the existence of the weak solutions for the p-Laplacian with strong resonance, which generalizes the previous results in one-dimension.
متن کاملExistence of a positive solution for one-dimensional singular p-Laplacian problems and its parameter dependence
Article history: Received 1 October 2013 Available online 21 November 2013 Submitted by J. Shi
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05485-4