In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

‎Using Nehari manifold methods and Mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.

a class of kirchhoff type systems with nonlinear boundary conditions considered in this paper. by using the method of nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

The existence of a connected 12-regular {K4, K2,2,2}-ultrahomogeneous graph G is established, (i.e. each isomorphism between two copies of K4 or K2,2,2 in G extends to an automorphism of G), with the 42 ordered lines of the Fano plane taken as vertices. This graph G can be expressed in a unique way both as the edge-disjoint union of 42 induced copies of K4 and as the edge-disjoint union of 21 i...