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Exact boundary behavior of large solutions to semilinear elliptic equations with a nonlinear gradient term

  • Zhijun ZhangEmail author
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Abstract

This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations Δu = b(x)f(u)(C0 + |∇u|q), x ∈ Ω, where Ω is a bounded domain with a smooth boundary in RN, C0 ≥ 0, q ∈ [0, 2), bC loc a (Ω) is positive in Ω, but may be vanishing or appropriately singular on the boundary, fC[0,1), f(0) = 0, and f is strictly increasing on [0;1) (or fC(R), f(s) > ∀ s ∈ R, f is strictly increasing on R). We show unified boundary behavior of such solutions to the problem under a new structure condition on f.

Keywords

semilinear elliptic equations a nonlinear gradient term large solutions boundary behavior 

MSC(2010)

35J25 35J65 35J67 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11571295). The author is greatly indebted to the anonymous referees for the very helpful suggestions and com- ments which improved the quality of the presentation.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesYantai UniversityYantaiChina

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