DOI: 10.14232/ejqtde.2026.1.58 ISSN: 1417-3875

Existence and multiplicity of positive solutions for nonlinear polyharmonic Dirichlet problems

Ruyun Ma, Xiangbing Lei, Jingxuan Wang
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In this paper, we are concerned with the existence and multiplicity of positive solutions for the following polyharmonic equations with Dirichlet boundary conditions { ( − Δ ) m u = λ f ( x , u ) + μ g ( x , u ) , in  B , u = ∂ ν u = ⋯ = ∂ ν m − 1 u = 0 , on  ∂ B , where B is the unit ball in ℝ N , and ν is the exterior unit normal vector on the boundary. We employ degree theory combined with a continuation theorem and an unfolding of the bifurcations from zero and from infinity to prove our result.

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