Semilinear elliptic equations with strong singularity

doi:10.7523/j.issn.2095-6134.2017.06.002

›› 2017, Vol. 34 ›› Issue (6): 660-666.DOI: 10.7523/j.issn.2095-6134.2017.06.002

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Semilinear elliptic equations with strong singularity

TAN Yuxin, SUN Yijing

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-09-07 Revised:2016-12-19 Online:2017-11-15
Supported by:
Supported by the National Nature Science Foundation of China (11571339)

Abstract

Abstract: We prove the existence of a positive H₀¹-solution for the equation-div(M(x) ▽u)=(f(x))/(u^p), where M(x) is a bounded elliptic matrix (i. e., there exists 0< α ≤ β such that M(x)ξ·ξ ≥ α|ξ|²,|M(x)|≤ β,∀x ∈ Ω,∀ξ ∈ Rⁿ), and-p <-1. The key to the work lies in establishing the validity and connection of two constraints which simplify the existence of a minimizer for the corresponding singular functional.

Key words: bounded elliptic matrix, weak solution, strong singularity

CLC Number:

O175.25

TAN Yuxin, SUN Yijing. Semilinear elliptic equations with strong singularity[J]. , 2017, 34(6): 660-666.

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Semilinear elliptic equations with strong singularity

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