Energy dependent potential problems for the one dimensional p-Laplacian operator

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.

STRONG 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...

LOWER 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...

Existence 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

Positive Solutions for Discrete Boundary Value Problems to One-Dimensional p-Laplacian with Delay