Abstract:In this paper, we study the existence of nontrivial solutions to a class fractional SchrR odinger equationsu.x/ u.y/ jx yj N C2s dy; x 2 R N is a fractional operator and s 2 .0; 1/. By using variational methods, we prove this problem has at least two nontrivial solutions in a suitable weighted fractional Sobolev space.

In this paper, using continued fraction, we provide a new quicker sequence convergent to Euler’s constant. We demonstrate the superiority of our new convergent sequences over DeTemple’s sequence, Mortici’s sequences, Vernescu’s sequence, and Lu’s sequence.