A resonance problem for the p-laplacian in ℝN
Date
2005-10-17
Authors
Izquierdo B., Gustavo
Lopez Garza, Gabriel
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We show the existence of a weak solution for the problem
-∆pu = λ1h(x)|u|p-2 u + α(x)g(u) + ƒ(x), u ∈ D1,p (ℝN),
where, 2 < p < N, λ1 is the first eigenvalue of the p-Laplacian on D1,p(ℝN) relative to the radially symmetric weight h(x) = h(|x|). In this problem, g(s) is a bounded function for all s ∈ ℝ, α ∈ L(p*)' (ℝN) ∩ L∞ (ℝN) and ƒ ∈ L(p*)' (ℝN). To establish an existence result, we employ the Saddle Point Theorem of Rabinowitz [9] and an improved Poincaré inequality from an article of Alziary, Fleckinger and Takáč [2].
Description
Keywords
Resonance, p-Laplacian, Improved Poincare inequality
Citation
Izquierdo B., G., & Lopez Garza, G. (2005). A resonance problem for the p-laplacian in ℝN. <i>Electronic Journal of Differential Equations, 2005</i>(112), pp. 1-8.
Rights
Attribution 4.0 International