ok... thanks Denis! I will do that.

So, does this imply that x'' = x^3 + t, x(0) = 0 = x(1) has a solution? If yes, how?

Ohh.. Thanks for the correction, Denis. Going by the notes which I was referring, I called it a 'problem' instead of 'method'. So, does that mean that the claim made in the second statement (x'' = f (t, x), x(a) = x(b), x (a) = x (b) and f : [a, b] × R → R has a solution) is true?

Damn... I am feeling stupid :-) Thank you very much for pointing that out!!

ohh... that explains it. Thanks. Also, can you please shed some light on the apriori bounds part? That is quite confusing for me.

no no ... I will get the book in my college library. Thank you very much for that reference!