Skip to main content
MathOverflow

Return to Question

deleted 4 characters in body
Source Link
Student
Student
  • 567
  • 4
  • 15

I have been recently reading Kwong's paper on the uniqueness of positive solutions for the equation $\Delta u-u+u^p=0$ in $\mathbb{R}^n$.

The authors show that the followingabove equation has a unique positive radial solution such that $u>0$ and $u'(r)<0$ under the assumption that $1<p<\frac{n+2}{n-2}$ when $n\geq 3.$

I was wondering if this equation or its radial solutions have been studied in the case when $p=\frac{n+2}{n-2}.$ In particular, can one expect to show the same result as Kwong in this case?

I have been recently reading Kwong's paper on the uniqueness of positive solutions for the equation $\Delta u-u+u^p=0$ in $\mathbb{R}^n$.

The authors show that the following equation has a unique positive radial solution such that $u>0$ and $u'(r)<0$ under the assumption that $1<p<\frac{n+2}{n-2}$ when $n\geq 3.$

I was wondering if this equation or its radial solutions have been studied in the case when $p=\frac{n+2}{n-2}.$ In particular, can one expect to show the same result as Kwong in this case?

I have been recently reading Kwong's paper on the uniqueness of positive solutions for the equation $\Delta u-u+u^p=0$ in $\mathbb{R}^n$.

The authors show that the above equation has a unique positive radial solution such that $u>0$ and $u'(r)<0$ under the assumption that $1<p<\frac{n+2}{n-2}$ when $n\geq 3.$

I was wondering if this equation or its radial solutions have been studied in the case when $p=\frac{n+2}{n-2}.$ In particular, can one expect to show the same result as Kwong in this case?

removed capitals from title
Link
YCor
YCor
  • 63.9k
  • 5
  • 187
  • 286

Existence of Ground State Solutionsground state solutions for the Critical Exponentcritical exponent

Source Link
Student
Student
  • 567
  • 4
  • 15

Existence of Ground State Solutions for the Critical Exponent

I have been recently reading Kwong's paper on the uniqueness of positive solutions for the equation $\Delta u-u+u^p=0$ in $\mathbb{R}^n$.

The authors show that the following equation has a unique positive radial solution such that $u>0$ and $u'(r)<0$ under the assumption that $1<p<\frac{n+2}{n-2}$ when $n\geq 3.$

I was wondering if this equation or its radial solutions have been studied in the case when $p=\frac{n+2}{n-2}.$ In particular, can one expect to show the same result as Kwong in this case?