On the solutions of quartic Diophantine equations

This is the authors' abstract. We don't add key points for this paper.

In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.