Why is my LED blinking? I have this simple push button schematic:

The idea is that the LED is on as long as the button stays pushed, with the switch closed.
The code is below:
int ledPin=10;
int switchPin=5;

void setup()

{
  Serial.begin(9600);
  pinMode(switchPin, INPUT);
  pinMode(ledPin,OUTPUT);

}
void loop()

{
  digitalWrite(ledPin,LOW);//DBG
  if (digitalRead(switchPin)==HIGH)
{
 digitalWrite(ledPin,HIGH);//DBG
 delay(500);
}
 if (digitalRead(switchPin)==LOW);
{
digitalWrite(ledPin,LOW);//DBG 
delay(200);
}
}

As I keep the button pressed, the LED blinks regularly, instead of staying on. Why?
I have tried using a capacitor between the switch and switchPin, with no change.
The beginning of your code in the loop:

void loop()  {
  digitalWrite(ledPin,LOW); //remove this line here
  if (digitalRead(switchPin)==HIGH)
{
     digitalWrite(ledPin,HIGH);//DBG
     delay(500);
}
 if (digitalRead(switchPin)==LOW);
 {
      digitalWrite(ledPin,LOW);//DBG 
       delay(200);
     }
}


Before your first if(digital read(switch pin) == HIGH)  you turn the LED off, and then you have a delay, which gives the blinking effect, remove that and it will not blink.