In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional ...In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.展开更多
In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>...In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>1 and 3<α+β<6.We prove the existence of a ground state solution for the above problem in which the nonlinearity is not 4-superlinear at infinity.Also,using a discreetness property of Palais-Smale sequences and the Krasnoselkii genus method,we obtain the existence of infinitely many geometrically distinct solutions in the case whenα,β≥2 and 4≤α+β<6.展开更多
文摘In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.
文摘In this paper,we study the coupled system of Kirchhoff type equations−(a+b∫R 3|∇u|2 dx)Δu+u=2αα+β|u|α−2 u|v|β,−(a+b∫R 3|∇v|2 dx)Δv+v=2βα+β|u|α|v|β−2 v,u,v∈H 1(R 3),x∈R 3,x∈R 3,where a,b>0,α,β>1 and 3<α+β<6.We prove the existence of a ground state solution for the above problem in which the nonlinearity is not 4-superlinear at infinity.Also,using a discreetness property of Palais-Smale sequences and the Krasnoselkii genus method,we obtain the existence of infinitely many geometrically distinct solutions in the case whenα,β≥2 and 4≤α+β<6.