In this paper using topological degree we study the existence of nontrivial solutions for a fractional differential equation involving integral boundary conditions. Here, the nonlinear term may be sign-changing and may also depend on the derivatives of the unknown function.

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In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.

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Let G be a Lie group and H its subgroup, and M q , N r two submanifolds of dimensions q, r, respectively, in the Riemannian homogeneous space G/H. A kinematic integral formula for the angle between the two intersected submanifolds is obtained. MSC: 52A20; 53C65