, Let us recall (v i ) i?? and (v i,m ) i?? the functions defined in Proposition 4.2. We firstly prove that (v i ) i?? is a subsolution of (4.1), then we show that for a fixed m 0 , (v i,m0 ) i?? is a supersolution of (4.1), finally by Perron's method we show that

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