scholarly journals Renormalized solutions for some nonlinear nonhomogeneous elliptic problems with Neumann boundary conditions and right hand side measure

2021 ◽  
Vol 39 (6) ◽  
pp. 81-103
Author(s):  
Elhoussine Azroul ◽  
Mohamed Badr Benboubker ◽  
Rachid Bouzyani ◽  
Houssam Chrayteh
Keyword(s):  
Boundary Conditions ◽  
Radon Measure ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Measure Data ◽  
Renormalized Solutions ◽  
Renormalized Solution ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions

Our aim in this paper is to study the existence of renormalized solution for a class of nonlinear p(x)-Laplace problems with Neumann nonhomogeneous boundary conditions and diuse Radon measure data which does not charge the sets of zero p(.)-capacity

scholarly journals Stability properties of Radon measure-valued solutions for a class of nonlinear parabolic equations under Neumann boundary conditions

2021 ◽  
Vol 6 (11) ◽  
pp. 12182-12224
Author(s):  
Quincy Stévène Nkombo ◽  
◽  
Fengquan Li ◽  
Christian Tathy ◽  
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Radon Measure ◽  
Neumann Boundary ◽  
Large Time Behavior ◽  
Neumann Boundary Conditions ◽  
Degenerate Parabolic Equations ◽  
Measure Data ◽  
Normal Vector ◽  
Time Behavior

<abstract><p>In this paper, we address the existence, uniqueness, decay estimates, and the large-time behavior of the Radon measure-valued solutions for a class of nonlinear strongly degenerate parabolic equations involving a source term under Neumann boundary conditions with bounded Radon measure as initial data.</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} u_{t} = \Delta\psi(u)+h(t)f(x, t) \ \ &amp;\text{in} \ \ \Omega\times(0, T), \\ \frac{\partial\psi(u)}{\partial\eta} = g(u) \ \ &amp;\text{on} \ \ \partial\Omega\times(0, T), \\ u(x, 0) = u_{0}(x) \ \ &amp;\text{in} \ \ \Omega, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ T &gt; 0 $, $ \Omega\subset \mathbb{R}^{N}(N\geq2) $ is an open bounded domain with smooth boundary $ \partial\Omega $, $ \eta $ is an outward normal vector on $ \partial\Omega $. The initial value data $ u_{0} $ is a nonnegative bounded Radon measure on $ \Omega $, the function $ f $ is a solution of the linear inhomogeneous heat equation under Neumann boundary conditions with measure data, and the functions $ \psi $, $ g $ and $ h $ satisfy the suitable assumptions.</p></abstract>

scholarly journals Existence of positive radial solutions for a class of nonlinear singular elliptic problems in annular domains

1992 ◽  
Vol 35 (3) ◽  
pp. 405-418 ◽  
Author(s):  
Zongming Guo
Keyword(s):  
Boundary Conditions ◽  
Degree Theory ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Radial Solutions ◽  
Positive Radial Solutions ◽  
Annular Domains ◽  
Radially Symmetric Solutions

We establish the existence of positive radially symmetric solutions of Δu+f(r,u,u′) = 0 in the domainR1<r<R0with a variety of Dirichlet and Neumann boundary conditions. The functionfis allowed to be singular when eitheru= 0 oru′ = 0. Our analysis is based on Leray-Schauder degree theory.

scholarly journals Nonresonance conditions on the potential for a nonlinear nonautonomous Neumann problem

2019 ◽  
Vol 38 (3) ◽  
pp. 79-96 ◽  
Author(s):  
Ahmed Sanhaji ◽  
A. Dakkak
Keyword(s):  
Boundary Conditions ◽  
Neumann Problem ◽  
Elliptic Problems ◽  
Neumann Boundary ◽  
Existence Results ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
First Eigenvalue ◽  
The First Eigenvalue

The aim of this paper is to establish the existence of the principal eigencurve of the p-Laplacian operator with the nonconstant weight subject to Neumann boundary conditions. We then study the nonresonce phenomena under the first eigenvalue and under the principal eigencurve, thus we obtain existence results for some nonautonomous Neumann elliptic problems involving the p-Laplacian operator.

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