We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0 as t→ +∞. The case where b(t) ∼ (1 + t) with p < 1 has recently been considered. The result is that the hyperbolic problem has a unique global solution, and t...

The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations electrons in cold plasma is considered. For some simplified formulation the problem, criterion existence global time solutions obtained. original sufficient condition loss smoothness found, as well solution to remain smooth at least $ 2 \pi $. In addition, it shown that...

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Continuity results are given for the tra...

This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established f...

We prove that a variational quasilinear elliptic equation admits a positive weak solution on R n. Our results extend to a wider class of equations some known results about semilinear and quasilinear problems: all the coefficients involved (also the ones in the principal part) depend both on the variable x and on the unknown function u; moreover, they are not homogeneous with respect to u.

We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.

For a class of quasilinear Schrödinger equations we establish the existence of ground states of soliton type solutions by a minimization argument.

Assuming that a system of quasilinear equations of gradient type admits a strict supersolution and a strict subsolution, we show that it also admits a positive solution.

We show the existence of nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. A nonexistence result is also given.