Infinitely many solutions to boundary value problems for a coupled system of fractional differential equations (Q2812411)

The paper studies the existence of weak solutions to the following coupled system of differential equations of Riemann-Liouville fractional order: NEWLINE\[NEWLINE _t D _T^\alpha (a(t)_0D_t^\alpha u(x)) = \lambda F_u(t,u(t,v(t))),\quad 0<t<T, NEWLINE\]NEWLINE NEWLINE\[NEWLINE _t D _T^\beta (b(t)_0D_t^\alpha v(x)) = \lambda F_v(t,u(t,v(t))),\quad 0<t<T, NEWLINE\]NEWLINE NEWLINE\[NEWLINE u(t) =u(T)=0,\quad v(0)=v(T)=0. NEWLINE\]NEWLINE The minimization results by Mawhin and Willem are used for the existence of at least one weak solution. Then a critical point theorem by Rabinowitz is applied for the existence of infinitely many solutions. Examples are provided for illustration.