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Michael Hardy
Michael Hardy
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I want to prove the uniqueness of the solution of the following problem: $$\eqalign{ & - d\Delta u + u = {u^p}{\text{ in }}\Omega \cr & u > 0{\text{ in }}\Omega \cr & \frac{{\partial u}}{{\partial \nu }} = 0{\text{ on }}\partial \Omega \cr} $$$$\eqalign{ & - d\,\Delta u + u = {u^p} \text{ in } \Omega \cr & u > 0 \text{ in } \Omega \cr & \frac{\partial u}{\partial \nu} = 0 \text{ on } \partial \Omega \cr} $$ with $\Omega$ is a bounded open in $R^n$, d$>0$$d>0$ and $p>1$. I tried the classical methods but without any success. Thanx.

I want to prove the uniqueness of the solution of the following problem: $$\eqalign{ & - d\Delta u + u = {u^p}{\text{ in }}\Omega \cr & u > 0{\text{ in }}\Omega \cr & \frac{{\partial u}}{{\partial \nu }} = 0{\text{ on }}\partial \Omega \cr} $$ with $\Omega$ is a bounded open in $R^n$, d$>0$ and $p>1$. I tried the classical methods but without any success. Thanx.

I want to prove the uniqueness of the solution of the following problem: $$\eqalign{ & - d\,\Delta u + u = {u^p} \text{ in } \Omega \cr & u > 0 \text{ in } \Omega \cr & \frac{\partial u}{\partial \nu} = 0 \text{ on } \partial \Omega \cr} $$ with $\Omega$ is a bounded open in $R^n$, $d>0$ and $p>1$. I tried the classical methods but without any success. Thanx.

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Gustave
Gustave
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Uniqueness problem for an elliptic system

I want to prove the uniqueness of the solution of the following problem: $$\eqalign{ & - d\Delta u + u = {u^p}{\text{ in }}\Omega \cr & u > 0{\text{ in }}\Omega \cr & \frac{{\partial u}}{{\partial \nu }} = 0{\text{ on }}\partial \Omega \cr} $$ with $\Omega$ is a bounded open in $R^n$, d$>0$ and $p>1$. I tried the classical methods but without any success. Thanx.