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- W4313377711 abstract "In this paper, we study a singular nonhomogenous biharmonic problem with Dirichlet boundary condition in Heisenberg group$ begin{equation*} left {begin{array}{ll} Delta^2_{{mathbb{H}^1}}u = frac{f(xi, u)}{rho(xi)^beta}+epsilon h(xi) &mbox{in} Omega, u = frac{partial u}{partial nu} = 0, &mbox{on} partialOmega, end{array} right. end{equation*} $where $ Omegasubset {mathbb{H}^1} $ is a bounded smooth domain, $ Delta^2_{{mathbb{H}^1}}u = Delta_{mathbb{H}^1}(Delta_{mathbb{H}^1}u) $ denotes the biharmonic operator in Heisenberg group $ mathbb{H}^1 = mathbb{C} times mathbb{R} $, $ 0leq beta < 4 $ with $ 4 $ is the homogeneous dimension of $ {mathbb{H}^1} $ and $ f:Omega times mathbb{R}rightarrow mathbb{R} $ is a continuous function which satisfies subcritical and critical exponential growth condition, $ h(xi)in (D_0^{2, 2}(Omega))^* $, $ h(xi)geq0 $ and $ h(xi) notequiv0 $, $ rho(xi) = (|z|^4+t^2)^{frac{1}{4}} $, $ xi = (z, t)in mathbb{H}^1 $ with $ z = (x, y)inmathbb{R}^{2} $, $ epsilon $ is a small positive parameter. We obtain the existence and multiplicity of solutions by the Ekeland variational principle, mountain pass theorem and singular Adams inequality in Heisenberg group." @default.
- W4313377711 created "2023-01-06" @default.
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- W4313377711 date "2023-01-01" @default.
- W4313377711 modified "2023-10-18" @default.
- W4313377711 title "Multiple solutions for a singular nonhomogenous biharmonic equation in Heisenberg group" @default.
- W4313377711 doi "https://doi.org/10.3934/cpaa.2022160" @default.
- W4313377711 hasPublicationYear "2023" @default.
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