We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.

In this paper, the authors study an optimal control problem for quasilinear elliptic PDEs with pointwise state constraints. Weak and strong optimality conditions of Pontryagin maximum principle type are derived. In proving these results, we penalized the state constraints and respectively use the Ekeland variational principle and an exact penalization method. In this paper, our aim is to prove ...

We consider a quasilinear elliptic system of equations with nondiagonal principal matrix and additional terms admitting quadratic nonlinearity in the gradient solution. Under one-sided condition on strongly nonlinear term, we study local smoothness (possibly, unbounded)

In this thesis we study so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear partial differential equations. The two-grid method is constructed by first solving the nonlinear system of equations stemming from the discontinuous Galerkin finite element method on a coarse mesh partition; then, this coarse solution is used to linearis...

Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the (p1,…, pn)-Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent three-critical-point theorem obtained by Ricceri. We also give some examples to illustrate the obtained results.

In this paper, we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nerahi manifold and by exploring some properties of the best Hardy-Sobolev constan...

Abstract. We consider a system of a semilinear hyperbolic functional differential equation (where the lower order terms contain functional dependence on the unknown functions) with initial and boundary conditions and a quasilinear elliptic functional differential equation (containing t as a parameter) with boundary conditions. Existence of solutions for t ∈ (0, T ) will be shown and some exampl...

For quasilinear integro-diierential equations of the form u t ?aA(u) = f, where a is a scalar singular integral kernel that behaves like t ? , 1 2 < 1 and A is a second order quasilinear elliptic operator in divergence form, solutions are found for which A(u) is integrable over space and time.