Question

Maximize $J[f] = \int_\mathbb{R} f(x)\log f(x)\,dx$ over smooth surjections $f : \mathbb{R}\to (0, \alpha)$ subject to $\int_\mathbb{R} f(x)\,dx = 1$.

score 149 · Answer 1 · 2015-07-23 18:38:56

149

Views

Maximize $J[f] = \int_\mathbb{R} f(x)\log f(x)\,dx$ over smooth surjections $f : \mathbb{R}\to (0, \alpha)$ subject to $\int_\mathbb{R} f(x)\,dx = 1$.

Published on 23 Jul 2015 - 18:38

score 103 · Answer 2 · 2015-07-26 05:15:53

103

Views

Fourier-like integral equation

Published on 26 Jul 2015 - 5:15

score 101 · Answer 3 · 2026-03-25 23:16:08

101

Views

Differential equation with shifited term

Published on 25 Mar 2026 - 23:16

score 64 · Answer 4 · 2015-08-05 19:11:36

64

Views

A Gronwall type inequality for Fredholm operators

Published on 05 Aug 2015 - 19:11

score 608 · Answer 5 · 2015-08-07 12:29:26

608

Views

prove $ \int_0^1 (1-x^p)^\frac{1}{q} \,dx = \int_0^1 (1-x^q)^\frac{1}{p} \,dx$

Published on 07 Aug 2015 - 12:29

score 387 · Answer 6 · 2015-08-12 05:34:26

387

Views

Solve integral equation by converting to differential equation

Published on 12 Aug 2015 - 5:34

score 187 · Answer 7 · 2015-08-12 16:26:34

187

Views

How can I solve this integral equation by converting it to a differential equation

Published on 12 Aug 2015 - 16:26

score 109 · Answer 8 · 2026-03-25 09:29:17

109

Views

How to solve this special case of Fredholm Integral Equation of the First Kind

Published on 25 Mar 2026 - 9:29

score 104 · Answer 9 · 2015-08-18 08:15:22

104

Views

How to find exact solution of this volterra equation?

Published on 18 Aug 2015 - 8:15

score 70 · Answer 10 · 2015-08-20 05:02:52

70

Views

Cosine Fourier series solution of semi-major axis nonlinear integral equaton

Published on 20 Aug 2015 - 5:02

score 69 · Answer 11 · 2015-08-30 10:50:34

69

Views

Love's equation $f(x)+\frac{1}{\pi} \int_{-1}^{1} \frac{f(t)}{1+(x-t)^2}dt=1, \ \ (|x|\geq 1)$

Published on 30 Aug 2015 - 10:50

score 1.5k · Answer 12 · 2015-09-10 01:38:42

1.5k

Views

Solving a Volterra Integral Equation of the 2nd Kind

Published on 10 Sep 2015 - 1:38

score 537 · Answer 13 · 2015-09-12 07:50:03

537

Views

Checking whether the function $u(x)=e^x$ solves the integral equation $u(x) + \lambda \int_0^1\sin(xt) u(t) dt=1$

Published on 12 Sep 2015 - 7:50

score 121 · Answer 14 · 2026-03-26 14:30:22

121

Views

Integrate $\int\frac{x+1}{x^{4}+6x^{2}+4x}dx$

Published on 26 Mar 2026 - 14:30

score 104 · Answer 15 · 2026-03-26 19:03:05

104

Views

Which method solves this integral equation? $\int_{-1}^{1}w(x)\,e^{tx}\,dx=6\left(\frac{\cosh(t)}{t^2}-\frac{\sinh(t)}{t^3}\right)$

Published on 26 Mar 2026 - 19:03

List Question

Maximize $J[f] = \int_\mathbb{R} f(x)\log f(x)\,dx$ over smooth surjections $f : \mathbb{R}\to (0, \alpha)$ subject to $\int_\mathbb{R} f(x)\,dx = 1$.

Fourier-like integral equation

Differential equation with shifited term

A Gronwall type inequality for Fredholm operators

prove $ \int_0^1 (1-x^p)^\frac{1}{q} \,dx = \int_0^1 (1-x^q)^\frac{1}{p} \,dx$

Solve integral equation by converting to differential equation

How can I solve this integral equation by converting it to a differential equation

How to solve this special case of Fredholm Integral Equation of the First Kind

How to find exact solution of this volterra equation?

Cosine Fourier series solution of semi-major axis nonlinear integral equaton

Love's equation $f(x)+\frac{1}{\pi} \int_{-1}^{1} \frac{f(t)}{1+(x-t)^2}dt=1, \ \ (|x|\geq 1)$

Solving a Volterra Integral Equation of the 2nd Kind

Checking whether the function $u(x)=e^x$ solves the integral equation $u(x) + \lambda \int_0^1\sin(xt) u(t) dt=1$

Integrate $\int\frac{x+1}{x^{4}+6x^{2}+4x}dx$

Which method solves this integral equation? $\int_{-1}^{1}w(x)\,e^{tx}\,dx=6\left(\frac{\cosh(t)}{t^2}-\frac{\sinh(t)}{t^3}\right)$

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