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High perturbations of a new Kirchhoff problem involving the p-Laplace operator

2021
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Boundary Value Problems
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AbstractIn the present work we are concerned with the existence and multiplicity of solutions for the following new Kirchhoff problem involving the p-Laplace operator: $$ \textstyle\begin{cases} - (a-b\int _{\Omega } \vert \nabla u \vert ^{p}\,dx ) \Delta _{p}u = \lambda \vert u \vert ^{q-2}u + g(x, u), & x \in \Omega , \\ u = 0, & x \in \partial \Omega , \end{cases} $$ { − ( a − b ∫ Ω | ∇ u | p d x ) Δ p u = λ | u | q − 2 u + g ( x , u ) , x ∈ Ω , u = 0 , x ∈ ∂ Ω , where $a, b > 0$ a , b > 0 ,

doi:10.1186/s13661-021-01566-x
fatcat:jgghi7vtcfgznhpr6w4mmxlpda