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Blow Up Points Of Solution Curves For A Semilinear Problem.pdf

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Preview of Blow up points of solution curves for a semilinear problem
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📊 Size: 169 KB
📄 Pages: 19 pages
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Summary

The equation is given by ∆u + λf(u) = 0 in a bounded smooth domain Ω, with u = 0 on the boundary. The function f satisfies certain conditions, including being continuously differentiable, having a positive derivative at 0, and having limits at infinity. The paper considers different types of functions f, including asymptotically superlinear, sublinear, and linear, and studies the behavior of the solution set Σ. The main results include: (1) for asymptotically sublinear f, the only blow-up point is ∞; (2) for (0, 1)-type f, the blow-up points are ∞ and λ1/f+; (3) for asymptotically superlinear f, there are partial results, including the existence of a blow-up point at 0 with a branch of positive solutions approaching (0, ∞) under certain conditions. The paper also discusses the relationship between blow-up points and the Fučík spectrum of the operator −∆.

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The equation is given by ∆u + λf(u) = 0 in a bounded smooth domain Ω, with u = 0 on the boundary.

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  • File Format: PDF
  • File Size: 169 KB
  • Pages: 19
  • Language: EN
  • Total Downloads: 79
  • Last Updated: 9 hours ago

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