Existence and Multiplicity of Solutions for a Class of Particular Boundary Value Poisson Equations

Songyue Yu and Baoqiang Yan
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Songyue Yu: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Baoqiang Yan: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Mathematics, 2022, vol. 10, issue 12, 1-19

Abstract: In this paper, a special class of boundary value problems, − ▵ u = λ u q + u r , in Ω , u > 0 , in Ω , n · ∇ u + g ( u ) u = 0 , on ∂ Ω , where 0 < q < 1 < r < N + 2 N − 2 and g : [ 0 , ∞ ) → ( 0 , ∞ ) is a nondecreasing C 1 function. Here, Ω ⊂ R N ( N ≥ 3 ) is a bounded domain with smooth boundary ∂ Ω and λ > 0 is a parameter. The existence of the solution is verified via sub- and super-solutions method. In addition, the influences of parameters on the minimum solution are also discussed. The second positive solution is obtained by using the variational method.

Keywords: sub and super solutions method; comparison principle; variational method; mountain pass theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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