Abstract We present an extension of the Livens variational principle (sometimes also referred to as Hamilton-Pontryagin principle) mechanical systems subject holonomic constraints. The newly proposed embodies index reduction in spirit often-applied GGL stabilization and thus may be termed “GGL principle”. Euler-Lagrange equations assume form differential-algebraic (DAEs) with differentiation tw...

The existence of solutions $u$ in $H^1(\mathbb R^N,\mathbb R^M)\cap H^2_{loc}(\mathbb R^M)$ a coupled semilinear system second order elliptic partial differential equations on $\mathbb R^N$ the form \[ \mathcal{P}[u] = f(x,u,\partial u), \quad x\in \mathbb R^N, \] under pointwise constraints is considered. problem studied via constructed suitable topological invariant, so-called constrained deg...