Multiple docker containers accessible by nginx rev

I'd like to run multiple docker containers on one host VM which would be accessible through only one domain. I wanted to use request url to differentiate between containers. To achieve this I'm trying to set nginx server as reverse proxy and run it in the container also listening on port 80.

Let's say I have two containers running on port 3000 and 4000. The routing would be following:

docker-host.example.com/3000 -> this will access container exposing port 3000
docker-host.example.com/4000 -> this will access container exposing port 4000

The thing is I'm currently stack even with trying to define static rule for such reverse proxy. It works fine without any location:

upstream application {
    server <docker container>:3000;
}

server {
        listen 80;

        location / {
            proxy_pass_header  Server;
            proxy_set_header   Host $http_host;
            proxy_redirect     off;
            proxy_set_header   X-Real-IP $remote_addr;
            proxy_set_header   X-Scheme $scheme;
            proxy_pass         http://application/;
        }
}

But when I add port location and try to access it using localhost:{nginx port}/3000/

upstream application {
    server <docker container>:3000;
}

server {
        listen 80;

        location /3000/ {
            proxy_pass_header  Server;
            proxy_set_header   Host $http_host;
            proxy_redirect     off;
            proxy_set_header   X-Real-IP $remote_addr;
            proxy_set_header   X-Scheme $scheme;
            proxy_pass         http://application/3000/;
        }
}

It seems that first resource (main html) is requested correctly, but any other depending resource (for example js or css needed for this site) is missing. If I examine request for those resources I have in logs:

09:19:20 [error] 5#5: *1 open() "/etc/nginx/html/public/css/fonts.min.css" failed (2: No such file or directory), client: 172.17.0.1, server: , request: "GET /public/css/fonts.min.css HTTP/1.1", host: "localhost:8455", referrer:"http://localhost:8455/3000/"

So request url is http://localhost:8455/public/css/fonts.min.css

Instead of http://localhost:8455/3000/public/css/fonts.min.css

Could I ask you for any suggestions ? Is this scenario possible ?

You can select a docker container per port, your example:

http://example.com:4000/css/fonts.min.css
http://example.com:3000/css/fonts.min.css

But there is another approach that I like more, because I think it is clearer, access to a docker container by domain name, e.g:

http://a.example.com/css/fonts.min.css
http://b.example.com/css/fonts.min.css

Whichever you choose, there is a project in github that helps you to implement docker multi-container reverse proxy: https://github.com/jwilder/nginx-proxy

I've written an example using docker-compose for a similar scenario at: http://carlosvin.github.io/posts/reverse-proxy-multidomain-docker/