Study of Some Non-linear Elliptic Problems with No Continuous Lower Order Terms in Orlicz Spaces

2016 ◽  
Vol 13 (6) ◽  
pp. 4867-4899 ◽  
Author(s):  
H. Moussa ◽  
M. Rhoudaf
Keyword(s):  
Lower Order ◽  
Orlicz Spaces ◽  
Elliptic Problems ◽  
Non Linear ◽  
Lower Order Terms

Renormalized solutions of non-linear elliptic problems with three lower-order terms and $ L^1$-data

2017 ◽  
Vol 81 (3) ◽  
pp. 463-480
Author(s):  
A Benkirane ◽  
M El Moumni ◽  
A Fri
Keyword(s):  
Lower Order ◽  
Elliptic Problems ◽  
Renormalized Solutions ◽  
Non Linear ◽  
Lower Order Terms

Quasilinear elliptic problems with singular and homogeneous lower order terms

2019 ◽  
Vol 179 ◽  
pp. 105-130 ◽  
Author(s):  
José Carmona ◽  
Tommaso Leonori ◽  
Salvador López-Martínez ◽  
Pedro J. Martínez-Aparicio
Keyword(s):  
Lower Order ◽  
Elliptic Problems ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

scholarly journals Solutions of nonlinear elliptic problems with lower order terms

2015 ◽  
Vol 6 (1) ◽  
pp. 34-53 ◽  
Author(s):  
Youssef Akdim ◽  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni
Keyword(s):  
Lower Order ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Lower Order Terms

scholarly journals $${W^{1,1}_0}$$ -solutions for elliptic problems having gradient quadratic lower order terms

2013 ◽  
Vol 20 (6) ◽  
pp. 1741-1757 ◽  
Author(s):  
David Arcoya ◽  
Lucio Boccardo ◽  
Tommaso Leonori
Keyword(s):  
Lower Order ◽  
Elliptic Problems ◽  
Lower Order Terms

scholarly journals Existence of solutions for some strongly nonlinear parabolic problems involving lower order terms in divergence form in Musielak-Orlicz spaces

2019 ◽  
Vol 38 (6) ◽  
pp. 99-126
Author(s):  
Abdeslam Talha ◽  
Abdelmoujib Benkirane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Strongly Nonlinear ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this work, we prove an existence result of entropy solutions in Musielak-Orlicz-Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data.

Existence and Regularizing Effect of Degenerate Lower Order Terms in Elliptic Equations Beyond the Hardy Constant

2018 ◽  
Vol 18 (4) ◽  
pp. 775-783 ◽  
Author(s):  
David Arcoya ◽  
Alexis Molino ◽  
Lourdes Moreno-Mérida
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Lower Order ◽  
Dirichlet Boundary Condition ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Model Problem ◽  
Elliptic Problems ◽  
Hardy Potential ◽  
Lower Order Terms

AbstractIn this paper, we study the regularizing effect of lower order terms in elliptic problems involving a Hardy potential. Concretely, our model problem is the differential equation-\Delta u+h(x)|u|^{p-1}u=\lambda\frac{u}{|x|^{2}}+f(x)\quad\text{in }\Omega,with Dirichlet boundary condition on {\partial\Omega}, where {p>1} and {f\in L^{m}_{h}(\Omega)} (i.e. {|f|^{m}h\in L^{1}(\Omega)}) with {m\geq\frac{p+1}{p}}. We prove that there is a solution of the above problem even for λ greater than the Hardy constant; i.e., {\lambda\geq\mathcal{H}=\frac{(N-2)^{2}}{4}} and nonnegative functions {h\in L^{1}(\Omega)} which could vanish in a subset of Ω. Moreover, we show that all the solutions are in {L^{pm}_{h}(\Omega)}. These results improve and generalize the case {h(x)\equiv h_{0}} treated in [2, 10].

The Regularizing Effect of Lower Order Terms in Elliptic Problems Involving Hardy Potential

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
A. Adimurthi ◽  
Lucio Boccardo ◽  
G. Rita Cirmi ◽  
Luigi Orsina
Keyword(s):  
Lower Order ◽  
Order Term ◽  
Elliptic Problems ◽  
Lower Order Term ◽  
Hardy Potential ◽  
Lower Order Terms

AbstractWe study existence and summability of solutions for elliptic problems with a power-like lower order term and a Hardy potential. We prove that, due to the presence of the lower order term, solutions exist and are more summable under weaker assumptions than those needed for the existence without it.

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