NONLINEAR FRACTIONAL SCHRO spacing diaeresis DINGER EQUATIONS COUPLED BY POWER-TYPE NONLINEARITIES

In this work, we study the following class of systems of coupled nonlinear fractional Schrodinger equations, {(-delta)(s)u(1 )+lambda(1)u(1) = mu(1)|u(1)|(2p-2)u(1) + beta|u(2)|(p)|u(1)|(p-2)u(1) in R-N, (-delta)(s)u(2 )+lambda(2)u(2) = mu(2)|u(2)|(2p-2)u(2) + beta|u(1)|(p)|u(2)|(p-2)u(2) in R-N, where u(1), u(2) is an element of W-s,W-2(R-N), with N = 1, 2, 3; lambda(j), mu(j) > 0, j = 1, 2, beta is an element of R, p >= 2 and p - 1/2p N < s < 1. Precisely, we prove the existence of positive radial bound and ground state solutions provided the parameters p, beta, lambda(j), mu(j), (j = 1, 2) satisfy appropriate conditions. We also study the previous system with m equations, (-delta)(s)u(j) + lambda(j)u(j) = mu(j)|u(j)|(2p-2)u(j) + sigma(m)(k=1k&NOTEQUexpressionL;j) beta(jk)|u(k)|(p)|u(j)|(p-2)u(j), uj is an element of W-s,W-2(R-N) where j = 1, ... , m >= 3, lambda(j), mu(j )> 0, the coupling parameters beta(jk) = beta(kj )is an element of R for j, k = 1, ... , m, j &NOTEQUexpressionL; k. For this system, we prove sim-ilar results as for m = 2, depending on the values of the parameters p, beta(jk), lambda(j), mu(j), (for j, k = 1,.. ., m, j &NOTEQUexpressionL; k).