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• W2032920027 abstract "In this paper, we study solutions of the equation −Δu=(u+)p in Ω⊂RN, where N+2N−2≤p<pc(N); see (3) for the definition of pc(N). We first classify all solutions (not necessarily bounded) having finite Morse index for Ω=RN or Ω=R+N with Dirichlet boundary condition. When Ω is a regular bounded domain of RN, for a family of solutions with Dirichlet boundary condition (un), we prove that ‖un‖L∞(Ω) is bounded if and only if the Morse index sequence, i(un), of un is bounded. Finally, we prove the same result for other nonlinearities f(x,u) which have similar growth respectively at ±∞." @default.
• W2032920027 created "2016-06-24" @default.
• W2032920027 creator A5030680412 @default.
• W2032920027 date "2011-02-01" @default.
• W2032920027 modified "2023-10-01" @default.
• W2032920027 title "Characterization of solutions having finite Morse index for some nonlinear PDE with supercritical growth" @default.
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• W2032920027 doi "https://doi.org/10.1016/j.na.2010.09.056" @default.
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