Advances in Differential Equations

Uniqueness of positive solutions with critical exponent and inverse square potential

Sanjiban Santra

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Abstract

We obtain the local uniqueness of positive solution for equation with inverse square terms in a smooth bounded domain. This is done by analyzing the Green function and the blow up profile of positive solution of some critical exponent problems with Hardy potential in a smooth bounded domain. We also determine the critical constant of the blow up behavior. This extends the result of Grossi [13] and Cerqueti [5] and Cao-Peng [3] to singular operators.

Article information

Source
Adv. Differential Equations Volume 19, Number 9/10 (2014), 879-910.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1404230127

Mathematical Reviews number (MathSciNet)
MR3229601

Zentralblatt MATH identifier
1311.35076

Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx] 35J35: Variational methods for higher-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations

Citation

Santra, Sanjiban. Uniqueness of positive solutions with critical exponent and inverse square potential. Adv. Differential Equations 19 (2014), no. 9/10, 879--910. https://projecteuclid.org/euclid.ade/1404230127.


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