Existence of positive solutions for two nonlinear eigenvalue problems
Rhouma, Nedra BelHaj
Southwest Texas State University, Department of Mathematics
We study the existence of positive solutions for the following two nonlinear eigenvalue problems ∆u - g(., u)u + λƒ(.,u) = 0, ∆u - g(., u)u + λƒ(., u) = 0, in a bounded regular domain in ℝ2 with u = 0 on the boundary. We assume that ƒ and g are in Kato class of functions.
Eigenvalue, Kato class, Green's function, Superharmonic function, Shauder fixed point theorem, Maximum principle
Rhouma, N. B., & Maatoug, L. (2003). Existence of positive solutions for two nonlinear eigenvalue problems. <i>Electronic Journal of Differential Equations, 2003</i>(16), pp. 1-16.