The Fredholm alternative for the one-dimensional p-Laplacian
نویسندگان
چکیده
منابع مشابه
A COUNTEREXAMPLE TO THE FREDHOLM ALTERNATIVE FOR THE p-LAPLACIAN
The following nonhomogeneous Dirichlet boundary value problem for the one-dimensional p-Laplacian with 1 < p < ∞ is considered: −(|u′|p−2u′)′ − λ|u|p−2u = f(x) for 0 < x < T ; u(0) = u(T ) = 0, (*) where f ≡ 1 + h with h ∈ L∞(0, T ) small enough. Solvability properties of Problem (*) with respect to the spectral parameter λ ∈ R are investigated. We focus our attention on some fundamental differ...
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...
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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 کاملRectifiability of Solutions of the One-dimensional P-laplacian
In the recent papers [8] and [10] a class of Carathéodory functions f(t, η, ξ) rapidly sign-changing near the boundary point t = a, has been constructed so that the equation −(|y′|p−2y′)′ = f(t, y, y′) in (a, b) admits continuous bounded solutions y whose graphs G(y) do not possess a finite length. In this paper, the same class of functions f(t, η, ξ) will be given, but with slightly different ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.03.077