Multiple Nontrivial Solutions for Nonlinear Eigenvalue Problems
نویسندگان
چکیده
In this paper we study a nonlinear eigenvalue problem driven by the p-Laplacian. Assuming for the right-hand side nonlinearity only unilateral and sign conditions near zero, we prove the existence of three nontrivial solutions, two of which have constant sign (one is strictly positive and the other is strictly negative), while the third one belongs to the order interval formed by the two opposite constant sign solutions. The approach relies on a combination of variational and minimization methods coupled with the construction of upper-lower solutions. The framework of the paper incorporates problems with concave-convex nonlinearities.
منابع مشابه
MULTIPLE SOLUTIONS FOR SEMILINEAR HEMIVARIATIONAL INEQUALITIES AT RESONANCE By LESZEK GASI\’{N}SKI AND NIKOLAOS
Abstract. We consider semilinear eigenvalue problems for hemivariational inequalities at resonance. First we consider problems which are at resonance in a higher eigenvalue $\lambda_{k}$ (with $k\geq 1$ ) and prove two multiplicity theorems asserting the existence of at least $k$ pairs of nontrivial solutions. Then we consider problems which are resonant at the first eigenvalue $\lambda_{1}>0$ ...
متن کاملExistence and Uniqueness of a Nontrivial Solution for Second Order Nonlinear m-Point Eigenvalue Problems on Time Scales
In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p ≥ 2, we study the existence and uniqueness of a nontrivial solution for nonlinear m-point eigenvalue problems on time scales. We obtain several sufficient conditions of the existence and uniqueness of nontrivial solution of the eigenvalue problems when λ is in some interval. Our approach is ba...
متن کاملNontrivial Solutions for Boundary Value Problems of Nonlinear Differential Equation
The nonlinear three-point boundary value problem { −u′′(t) = f(t, u(t)), t ∈ I, βu(0)− γu′(0) = 0, u(1) = αu(η), is discussed under some conditions concerning the first eigenvalue corresponding to a special linear operator, where I = [0, 1], η ∈ (0, 1), α, β, γ ∈ [0,∞) with β + γ 6= 0, f : [0, 1] × (−∞,+∞) → (−∞,+∞) is sign–changing continuous function and may be unbounded from below. By applyi...
متن کاملNontrivial Solutions for Singular Nonlinear Three-Point Boundary Value Problems
The singular nonlinear three-point boundary value problems { −(Lu)(t) = h(t)f (u(t)), 0 < t < 1, βu(0)− γ u′(0) = 0, u(1) = αu(η) are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u′(t))′+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be nonnegative. The associated ...
متن کاملNodal solutions of nonlinear elliptic Dirichlet problems on radial domains
Let Ω ⊂ R be a ball or an annulus and f : R → R absolutely continuous, superlinear, subcritical, and such that f(0) = 0. We prove that the least energy nodal solution of −∆u = f(u), u ∈ H 0 (Ω), is not radial. We also prove that Fučik eigenfunctions, i. e. solutions u ∈ H 0 (Ω) of −∆u = λu − μu−, with eigenvalue (λ, μ) on the first nontrivial curve of the Fučik spectrum, are not radial. A relat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007