Static spherically symmetric solutions in SU(N)-EYM and EYMD theories are classified by the node numbers of their non-trivial gauge field functions. With increasing node numbers, the solutions form sequences, tending to limiting solutions. The limiting solutions are based on subalgebras of su(N), consisting of a neutral non-abelian part and a charged abelian part, belonging to the Cartan subalg...

We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kähler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kählerity of our solutions.

A. We consider the semi-linear elliptic PDEs driven by the fractional Laplacian: { (−∆)su = f (x, u), in Ω, u = 0, in Rn\Ω. By the Mountain Pass Theorem and some other nonlinear analysis methods, the existence and multiplicity of non-trivial solutions for the above equation are established. The validity of the Palais-Smale condition without AmbrosettiRabinowitz condition for non-local el...

Abstract The Mathieu–Duffing equation represents a basic form for parametrically excited system with cubic nonlinearities. In multi-degree-of-freedom systems, parametric resonances and the associated limit cycles take place at both principal combination resonance frequencies. Furthermore, using asynchronous excitation of coupling terms leads to broadband destabilization trivial solution appeara...