Discontinuous Galerkin (DG) methods are studied for solving an elliptic variational inequality of 4th-order. Numerous discontinuous Galerkin schemes for the Kirchhoff plate bending problem are extended to the variational inequality. Numerical results are presented to illustrate convergence orders of the different methods.

A Kirchhoff elliptic vortex is a two-dimensional elliptical region of uniform vorticity embedded in an inviscid, incompressible, and irrotational fluid. By using analytic theory and contour dynamics simulations, we describe the evolution of perturbed Kirchhoff vortices by decomposing solutions into constituent linear eigenmodes. With small amplitude perturbations, we find excellent agreement be...

In this paper we study a non-homogeneous elliptic Kirchhoff equation with nonlinear reaction term. We analyze the existence and uniqueness of positive solution. The main novelty is the inclusion of non-homogeneous term making the problem without a variational structure. We use mainly bifurcation arguments to get the results.

Abstract In this paper, we study a class of ( p , q )-Schrödinger–Kirchhoff type equations involving continuous positive potential satisfying del Pino–Felmer conditions and nonlinearity with subcritical growth at infinity. By applying variational methods, penalization techniques Lusternik–Schnirelman category theory, relate the number solutions topology set where attains its minimum values.