Existence of weak positive solutions in anisotropic Musielak–Orlicz–Sobolev spaces for (μ(·), ν(·))-Laplacian-type Kirchhoff models

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Abstract The primary objective of this paper is to study the existence of infinitely many positive weak solutions for a class of double-phase ( μ → ⁢ ( ⋅ ) , ν → ⁢ ( ⋅ ) ) (\vec{\mu}(\,\cdot\,),\vec{\nu}(\,\cdot\,)) -Kirchhoff-type problems governed by the following elliptic Kirchhoff equation with Dirichlet boundary conditions: { - ∑ i = 1 N ℜ i ⁢ ( ∫ 𝒰 ( 1 μ i ⁢ ( s ) ⁢ | ∂ ⁡ ξ ⁢ ( s ) ∂ ⁡ s i | μ i ⁢ ( s ) + 1 ν i ⁢ ( s )