Sample sketch for demonstrating ESP connection to Blynk local server.

BlynkLocalSample.ino

/*************************************************************
  Download latest Blynk library here:
    https://github.com/blynkkk/blynk-library/releases/latest

  Blynk is a platform with iOS and Android apps to control
  Arduino, Raspberry Pi and the likes over the Internet.
  You can easily build graphic interfaces for all your
  projects by simply dragging and dropping widgets.

    Downloads, docs, tutorials: http://www.blynk.cc
    Sketch generator:           http://examples.blynk.cc
    Blynk community:            http://community.blynk.cc
    Follow us:                  http://www.fb.com/blynkapp
                                http://twitter.com/blynk_app

  Blynk library is licensed under MIT license
  This example code is in public domain.

 *************************************************************

      Sample sketch to connect ESP device to Local Server
 *************************************************************/

/* Comment this out to disable prints and save space */
#define BLYNK_PRINT Serial

/* Fill-in your Template ID (only if using Blynk.Cloud) */
//#define BLYNK_TEMPLATE_ID   "YourTemplateID"


#include <ESP8266WiFi.h>
#include <BlynkSimpleEsp8266.h>

// You should get Auth Token in the Blynk App.
// Go to the Project Settings (nut icon).
char auth[] = "ENTER YOUR AUTHENTICATION TOKEN HERE";

// Your WiFi credentials.
// Set password to "" for open networks.
char ssid[] = "ENTER YOUR WIFI SSID HERE";
char pass[] = "ENTER YOUR WIFI PASSWORD HERE";



// This function will be called every time Slider Widget
// in Blynk app writes values to the Virtual Pin V1
BLYNK_WRITE(V1)
{ 
  // assigning incoming value from pin V1 to a variable
  int pinValue = param.asInt(); 
  digitalWrite(LED_BUILTIN, pinValue);
  // process received value
}

void setup()
{ 
  pinMode(LED_BUILTIN, OUTPUT);
  // Debug console
  Serial.begin(115200);                  

  // Blynk.begin(auth, ssid, pass);
  // You can also specify server:
  // Blynk.begin(auth, ssid, pass, "blynk-cloud.com", 80);
  // Change the IP address to match the IP address of your local server
  Blynk.begin(auth, ssid, pass, IPAddress(192,168,0,5), 8080);
}

void loop()
{
  Blynk.run();
}