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

Abstract

In this paper, a special class of boundary value problems, −▵u=λuq+ur,inΩ,u>0, inΩ,n·∇u+g(u)u=0,on∂Ω, where 0q1rN+2N−2 and g:[0,∞)→(0,∞) is a nondecreasing C1 function. Here, Ω⊂RN(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