Invariant sample measures and random Liouville type theorem for a nonautonomous stochastic <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-Laplacian equation

Invariant measures for a stochastic Kuramoto-Sivashinky equation

For the 1-dimensional Kuramoto–Sivashinsky equation with random forcing term, existence and uniqueness of solutions is proved. Then, the Markovian semigroup is well defined; its properties are analyzed, in order to provide sufficient conditions for existence and uniqueness of invariant measures for this stochastic equation. Finally, regularity results are obtained by means of Girsanov theorem.

p-Laplacian Type Equations Involving Measures

This is a survey on problems involving equations −divA(x,∇u) = μ, where μ is a Radon measure and A : Rn ×Rn → Rn verifies Leray-Lions type conditions. We shall discuss a potential theoretic approach when the measure is nonnegative. Existence and uniqueness, and different concepts of solutions are discussed for general signed measures. 2000 Mathematics Subject Classification: 35J60, 31C45.

Existence of Random Attractors for a p-Laplacian-Type Equation with Additive Noise

and Applied Analysis 3 introducing a new inner product over the resolvent of Laplacian, we surmount this obstacle and obtain the estimate of the solution in the Sobolev space V0, which is weaker than V , see Lemma 4.2 in Section 4. Here some basic results about Dirichlet forms of Laplacian are used. For details on the Dirichlet forms of a negative definite and self-adjoint operator please refer...

Invariant measures for Burgers equation with stochastic forcing

A Liouville-type theorem for Schrödinger operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P1, such that a nonzero subsolution of a symmetric nonnegative operator P0 is a ground state. Particularly, if Pj := −∆ + Vj , for j = 0, 1, are two nonnegative Schrödinger operators defined on Ω ⊆ R such that P1 is critical in Ω with a ground state φ, the function ψ 0 is a...