Let $\lambda>1$ and show the equation $\lambda - z -e^{-z} = 0$ has exacly one solution in the half plane $\{z:Re(z)>0\}$
124300
$\lambda-z-e^{-z}=0$ has one solution in the right half plane
91003
Prove that equation has exactly 2 solutions
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
131120
Proving an integral equation.
54703
Find the a < 0 for which the inequalities have at least one common solutions
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
98282
Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
120774
Show that $f$ has exactly one zero on the square $Q =$ {$x + iy ∈ \Bbb C : |x| < 1, |y| < 1$}.
121765
Semigroups and solutions of equation
66409
Show that the linear operator $(Tf)(x)=\frac{1}{\pi} \int_0^{\infty} \frac{f(y)}{(x+y)} dy$ satisfies $\|T\|\leq 1$.
48686
Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.
32209
Labeling solutions of an Eigenvalue equation involving Bessel functions
100968
Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?