On some general multiplying solutions results of a Robin problem

2020/12/12 by Aydin, Ismail, Unal, Cihan
#35J70 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 35J35 #Secondary 35J60

paper · doi:10.48550/arxiv.2012.06879

Abstract

By applying Ricceri's variational principle, we demonstrate the existence of solutions for the following Robin problem \ -\funcdiv( ω₁(x)\vert ∇ u\vert^p(x)-2∇ u) =λω₂(x)f(x,u), · amp; x∈ Ω
ω₁(x)\vert ∇ u\vert ^p(x)-2(∂ u)/( ∂ υ )+β(x)\vert u\vert ^p(x)-2u=0, · amp; x∈ ∂ Ω, . in W_ω₁,ω₂^1,p(.)( Ω) under some appropriate conditions.

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