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تسجيل مستخدم جديدMulti-bubble nodal solutions to slightly subcritical elliptic problems with Hardy terms
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The paper is concerned with the slightly subcritical elliptic problem with Hardy term [ left{ begin{aligned} -Delta u-mufrac{u}{|x|^2} &= |u|^{2^{ast}-2-epsilon}u &&quad text{in } Omega, u &= 0&&quad text{on } partialOmega, end{aligned} right. ] in a bounded domain $Omegasubsetmathbb{R}^N$ with $0inOmega$, in dimensions $Nge7$. We prove the existence of multi-bubble nodal solutions that blow up positively at the origin and negatively at a different point as $epsilonto0$ and $mu=epsilon^alpha$ with $alpha>frac{N-4}{N-2}$. In the case of $Omega$ being a ball centered at the origin we can obtain solutions with up to $5$ bubbles of different signs. We also obtain nodal bubble tower solutions, i.e. superpositions of bubbles of different signs, all blowing up at the origin but with different blow-up order. The asymptotic shape of the solutions is determined in detail.
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