Multiple solutions of systems of fractional boundary value problems

Abstract

The authors discuss the existence of multiple solutions of the system of fractional boundary value problems of the formwhere , is a parameter, , and are, respectively, the left and right Riemann–Liouville fractional integrals of order , and is a given function. Using critical point theory, sufficient conditions are found under which the above problem has at least two or infinitely many nontrivial solutions.

Keywords:

• multiple solutions
• fractional boundary value problem
• variational methods
• mountain pass lemma
• Cerami’s condition
• fountain theorem

AMS Subject Classifications:

• 34B15
• 34A08

Additional information

Funding

The research of Q. Kong was supported in part by the NNSF of China [grant number 11271379].