要解决“API网关没有HTTPS时DNS无法工作”的问题，您可以使用以下代码示例中的解决方法之一：

1. 使用Node.js和express框架的例子：

const express = require('express');
const https = require('https');
const http = require('http');

const app = express();

// 启用HTTPS
const httpsServer = https.createServer(app);

// 启用HTTP
const httpServer = http.createServer(app);

// 设置API路由
app.get('/api/example', (req, res) => {
  // 处理API请求
});

// 启动HTTP服务器
httpServer.listen(80, () => {
  console.log('HTTP Server running on port 80');
});

// 启动HTTPS服务器
httpsServer.listen(443, () => {
  console.log('HTTPS Server running on port 443');
});

2. 使用Java和Spring Boot框架的例子：

import org.springframework.boot.SpringApplication;
import org.springframework.boot.autoconfigure.SpringBootApplication;
import org.springframework.boot.web.servlet.ServletRegistrationBean;
import org.springframework.boot.web.servlet.support.SpringBootServletInitializer;
import org.springframework.context.annotation.Bean;
import org.springframework.web.servlet.DispatcherServlet;

@SpringBootApplication
public class ApiGatewayApplication extends SpringBootServletInitializer {

    public static void main(String[] args) {
        SpringApplication.run(ApiGatewayApplication.class, args);
    }

    @Bean
    public ServletRegistrationBean dispatcherServlet() {
        ServletRegistrationBean servletBean = new ServletRegistrationBean<>();
        servletBean.setServlet(new DispatcherServlet());
        servletBean.addUrlMappings("/api/*"); // 设置API路由
        return servletBean;
    }
}

这些示例中的代码将启动一个带有HTTP和HTTPS支持的服务器，并设置了一个API路由。您可以根据您的需求进行修改和自定义。