Nonlinear evolution problems with singular coefficients in the lower order terms

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Nagumo theorems of third-order singular nonlinear boundary value problems

*Correspondence: [email protected] Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P.R. China College of Mathematics, Jilin University, Changchun, 130012, P.R. China Abstract In this paper, we establish the Nagumo theorems for boundary value problems associated with a class of third-order singular nonlinear equations: (p(t)x′)′′ = f (t, x,p(t)x′, (p(t)x′)′), ∀t ...

Title AN L^p-APPROACH TO SINGULAR LINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

Exact Controllability for Problems of Transmission of the Plate Equation with Lower-order Terms

We consider the exact controllability for the problem of transmission of the plate equation with lower-order terms. Using Lions’ Hilbert Uniqueness Method (HUM for short), we show that the system is exactly controllable in L(Ω) ×H−2(Ω) . We also obtain some uniqueness theorems for the problem of transmission of the plate equation and for the operator a(x)∆ + q .

Boundary value problems for elliptic operators with singular drift terms

Let Ω be a Lipschitz domain in R, n ≥ 3, and L = divA∇ − B∇ be a second order elliptic operator in divergence form with real coefficients such that A is a bounded elliptic matrix and the vector field B ∈ Lloc(Ω) is divergence free and satisfies the growth condition dist(X, ∂Ω)|B(X)| ≤ ε1 for ε1 small in a neighbourhood of ∂Ω. For these elliptic operators we will study on the basis of the theory...