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- W2797719044 abstract "Abstract In the present paper, we investigate the existence of solutions for the following inhomogeneous singular equation involving the {p(x)} -biharmonic operator: left{begin{aligned} &displaystyleDelta(lvertDelta urvert^{p(x)-2}% Delta u)=g(x)u^{-gamma(x)}mplambda f(x,u)&&displaystylephantom{}text{in% }Omega, &displaystyleDelta u=u=0&&displaystylephantom{}text{on }partialOmega,% end{aligned}right. where {Omegasubsetmathbb{R}^{N}} ( {Ngeq 3} ) is a bounded domain with {C^{2}} boundary, λ is a positive parameter, {gamma:overline{Omega}rightarrow(0,1)} is a continuous function, {pkern-1.0ptinkern-1.0ptC(overline{Omega})} with {1kern-1.0pt<kern-1.0ptp^{-}kern-1.0pt:=kern-1.0ptinf_{xinOmega}p(x)% kern-1.0ptleqkern-1.0ptp^{+}kern-1.0pt:=kern-1.0ptsup_{xinOmega}p(x)% kern-1.0pt<kern-1.0ptfrac{N}{2}} , as usual, {p^{*}(x)kern-1.0pt=kern-1.0ptfrac{Np(x)}{N-2p(x)}} , gin L^{frac{p^{*}(x)}{p^{*}(x)+gamma(x)-1}}(Omega), and {f(x,u)} is assumed to satisfy assumptions (f1)–(f6) in Section 3. In the proofs of our results, we use variational techniques and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces. In addition, an example to illustrate our result is given." @default.
- W2797719044 created "2018-04-24" @default.
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- W2797719044 date "2018-03-13" @default.
- W2797719044 modified "2023-09-26" @default.
- W2797719044 title "On the existence of a weak solution for some singular p ( x ) p(x) -biharmonic equation with Navier boundary conditions" @default.
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- W2797719044 doi "https://doi.org/10.1515/anona-2016-0260" @default.
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