On some nonlinear elliptic systems with coercive perturbations in RN

A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN: Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN . Existence of nontrivial solutions is obtained by applying critical point the ory; also a regularity result is established. 2000 Mathematics Sub ject Classification: 35J70, 35B45, 35B65

Estimates on counting functions associated to some hyperbolic operators and spectral properties

We study the distribution of the eigenvalues of a linear operator associated to a hyperbolic partial differential equation with periodic boundary conditions. Using some recent results concerning the distributions of the values of indefinite quadratic forms at integers, we are able to derive the equidistribution of the eigenvalues relatively to the Lebesgue measure with exact asymptotics. Also we provide an asymptotic lower bound in the rational case

Existence results for double phase problems depending on Robin and Steklov eigenvalues for the p-Laplacian

In this paper we study double phase problems with nonlinear boundary condition and gradient dependence. Under quite general assumptions we prove existence results for such problems where the perturbations satisfy a suitable behavior in the origin and at infinity. Our proofs make use of variational tools, truncation techniques and comparison methods. The obtained solutions depend on the first eigenvalues of the Robin and Steklov eigenvalue problems for the p-Laplacian

A note on some elliptic equations of anisotropic type

We prove the existence of weak solutions to some nonlinear elliptic equations governed by an anisotropic operator mapping an appropriate function space to its dual. A sign condition with no growth restrictions with respect to the variable solution is imposed to a perturbed nonlinear term to the operator. The data is considered to be close to L^1

Parabolic problems in non-standard Sobolev spaces of infinite order

This paper is devoted to the study of the existence of solutions for the strongly nonlinear $p(x)$-parabolic equation$$\frac{\partial u}{\partial t} + Au + g(x,t,u) = f(x,t),$$where $A$ is a Leray-Lions operator acted from $V^{\infty,p(x)}(a_\alpha,Q_{T})$ into its dual. The nonlinear term $\>g(x,t,s)\>$ satisfies growth and sign conditions and the datum $\>f\>$ is assumed to be in the dual space $V^{-\infty,p'(x)}(a_\alpha,Q_{T})\>.

Parabolic Equations of Infinite Order with 1 Data

We prove an existence result of a nonlinear parabolic equation under Dirichlet null boundary conditions in Sobolev spaces of infinite order, where the second member belongs to 1 ( )

Anisotropic elliptic equations in RN\mathbb R^{N}: existence and regularity results

We investigate a class of anisotropic elliptic equations in the whole $\mathbb R^N$. By a variational approach, we obtain existence and regularity of nontrivial solutions in the framework of anisotropic Sobolev spaces. In addition, when the data is assumed to be merely locally integrable, the existence of solutions is established for a subclass of equations

On some nonlinear elliptic systems with coercive perturbation in RN

A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN. Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established