Existence and multiplicity of positive radial solutions to the Dirichlet problem for nonlinear elliptic equations on annular domains
DOI:
https://doi.org/10.24193/subbmath.2020.1.09Keywords:
Positive solution, elliptic equations, existence, multiplicity, local boundary, Green’s function.Abstract
In this paper, we study the existence and nonexistence of monotone positive radial solutions of elliptic boundary value problems on bounded annular domains subject to local boundary condition. By using Krasnoselskii’s fixed point theorem of cone expansion-compression type we show that there exists λ∗ ≥ λ∗ > 0 such that the elliptic equation has at least two, one and no radial positive solutions for 0 < λ ≤ λ∗, λ∗ < λ ≤ λ∗ and λ > λ∗ respectively. We include an example to illustrate our results.
Mathematics Subject Classification (2010): 35J25, 34B18.
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