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FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS 被引量:2
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作者 yaghoub jalilian 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1317-1330,共14页
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
关键词 fractional integral inequality existence of solution Caputo fractional derivative fractional differential equation fixed point
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EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A COUPLED SYSTEM OF KIRCHHOFF TYPE EQUATIONS
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作者 yaghoub jalilian 《Acta Mathematica Scientia》 SCIE CSCD 2020年第6期1831-1848,共18页
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
关键词 Kirchhoff equation Nehari-Pohožave manifold constrained minimization ground state solution
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