Hello everyone,
after having read the PIC32MX UART and interrupt documentation I can't fix the problem and I'm stuck with my project. That is, how to mange the TX Interrut Service Routine using PIC32MX795F512L. In the sense that, once I configure UART2 to generate interrupt after data transmission, the UART TX ISR is continuously called and U2TXIF is always 1, even if I reset it with an instruction at the end of the UART ISR.

I explain better my problem with the UART example present in MPLAB C32 Suite, which can be open through "uart_interrupt.mcp" project file. To test this project I'm using Microchip Explorer 16 Demo Board.
In this project, originally, it's just enabled the UART RX interrupt (instruction INTEnable(INT_SOURCE_UART_RX(UART2), INT_ENABLED)). Therefore, to trigger the ISR also when I transmit a character, after that instruction I added the corresponding INTEnable(INT_SOURCE_UART_TX(UART2), INT_ENABLED) one. But in this case the project doesn't work properly, because ISR(_UART2_VECTOR, ipl2) IntUart2Handler(void) ISR function is continuously called. I attach the related code to be more clear. In this code I didn't add all the code I need to manage character transmission, because before I have to properly manage the UART TX ISR operation.

Please, since I don't find a solution to this problem and I'm stuck on the project, can anyone help me? Many many thanks!

Code:
#include                     // Peripheral Library


// *****************************************************************************
// *****************************************************************************
// Section: Configuration bits
// SYSCLK = 80 MHz (8MHz Crystal/ FPLLIDIV * FPLLMUL / FPLLODIV)
// PBCLK = 40 MHz
// Primary Osc w/PLL (XT+,HS+,EC+PLL)
// WDT OFF
// Other options are don't care
// *****************************************************************************
// *****************************************************************************
#pragma config FPLLMUL = MUL_20, FPLLIDIV = DIV_2, FPLLODIV = DIV_1, FWDTEN = OFF
#pragma config POSCMOD = HS, FNOSC = PRIPLL, FPBDIV = DIV_1

// *****************************************************************************
// *****************************************************************************
// Section: System Macros
// *****************************************************************************
// *****************************************************************************
#define    GetSystemClock()             (80000000ul)
#define    GetPeripheralClock()        (GetSystemClock()/(1 << OSCCONbits.PBDIV))
#define    GetInstructionClock()        (GetSystemClock())

#define DESIRED_BAUDRATE        (9600)      //The desired BaudRate


void WriteString(const char *string);

int main(void)
{

    // Configure the device for maximum performance but do not change the PBDIV
    // Given the options, this function will change the flash wait states, RAM
    // wait state and enable prefetch cache but will not change the PBDIV.
    // The PBDIV value is already set via the pragma FPBDIV option above..
    SYSTEMConfig(GetSystemClock(), SYS_CFG_WAIT_STATES | SYS_CFG_PCACHE);

    mPORTAClearBits(BIT_7);         // Turn off RA7 on startup.
    mPORTASetPinsDigitalOut(BIT_7);    // Make RA7 as output.


    // Explorer-16 uses UART2 to connect to the PC.
    // This initialization assumes 36MHz Fpb clock. If it changes,
    // you will have to modify baud rate initializer.
    UARTConfigure(UART2, UART_ENABLE_PINS_TX_RX_ONLY);
    UARTSetFifoMode(UART2, UART_INTERRUPT_ON_TX_NOT_FULL | UART_INTERRUPT_ON_RX_NOT_EMPTY);
    UARTSetLineControl(UART2, UART_DATA_SIZE_8_BITS | UART_PARITY_NONE | UART_STOP_BITS_1);
    UARTSetDataRate(UART2, GetPeripheralClock(), DESIRED_BAUDRATE);
    UARTEnable(UART2, UART_ENABLE_FLAGS(UART_PERIPHERAL | UART_RX | UART_TX));

    // Configure UART2 RX Interrupt
    INTEnable(INT_SOURCE_UART_RX(UART2), INT_ENABLED);
    INTSetVectorPriority(INT_VECTOR_UART(UART2), INT_PRIORITY_LEVEL_2);
    INTSetVectorSubPriority(INT_VECTOR_UART(UART2), INT_SUB_PRIORITY_LEVEL_0);
     
    /*** CODE I ADDED TO MICROCHIP EXAMPLE ***/

     // Configure UART2 TX Interrupt
     INTEnable(INT_SOURCE_UART_TX(UART2), INT_ENABLED);                           
     INTSetVectorPriority(INT_VECTOR_UART(UART2), INT_PRIORITY_LEVEL_2);
     INTSetVectorSubPriority(INT_VECTOR_UART(UART2), INT_SUB_PRIORITY_LEVEL_0);
 
   /*** END CODE I ADDED TO MICROCHIP EXAMPLE ***/

    // configure for multi-vectored mode
    INTConfigureSystem(INT_SYSTEM_CONFIG_MULT_VECTOR);

    // enable interrupts
    INTEnableInterrupts();


   WriteString("*** UART Interrupt-driven Application Example ***\r\n");
   WriteString("*** Type some characters and observe echo and RA7 LED toggle ***\r\n");


    // Let interrupt handler do the work
    while (1);

    return 0;
}
// helper functions
void WriteString(const char *string)
{
    while(*string != '\0')
    {
        while(!UARTTransmitterIsReady(UART2))
            ;

        UARTSendDataByte(UART2, *string);

        string++;

        while(!UARTTransmissionHasCompleted(UART2))
            ;
    }
}
void PutCharacter(const char character)
{
        while(!UARTTransmitterIsReady(UART2))
            ;

        UARTSendDataByte(UART2, character);


        while(!UARTTransmissionHasCompleted(UART2))
            ;
}

// UART 2 interrupt handler
// it is set at priority level 2
void __ISR(_UART2_VECTOR, ipl2) IntUart2Handler(void)
{
    // Is this an RX interrupt?
    if(INTGetFlag(INT_SOURCE_UART_RX(UART2)))
    {
        // Clear the RX interrupt Flag
        INTClearFlag(INT_SOURCE_UART_RX(UART2));

        // Echo what we just received.
        PutCharacter(UARTGetDataByte(UART2));

        // Toggle LED to indicate UART activity
        mPORTAToggleBits(BIT_7);
    }

    // We don't care about TX interrupt
    if ( INTGetFlag(INT_SOURCE_UART_TX(UART2)) )
    {
        INTClearFlag(INT_SOURCE_UART_TX(UART2));
    }
}