scholarly journals Anisotropic nonlinear problem of infinite order with variables exponents and $L^1$ data

2020 ◽  
Author(s):  
Moussa Chrif ◽  
hakima ouyahya
Keyword(s):  
Nonlinear Equation ◽  
Elliptic Operator ◽  
Nonlinear Problem ◽  
Sobolev Spaces ◽  
Lower Order ◽  
Infinite Order ◽  
Existence Of Solutions ◽  
Order Term ◽  
Strongly Nonlinear ◽  
Sign Condition

In this paper, we prove the existence of solutions for the strongly nonlinear equation of the type $$Au+g(x,u)=f$$ where $A$ is an elliptic operator of infinite order from a functional Sobolev spaces of infinite order with variables exponents to its dual. $g(x, s)$ is a lower order term satisfying essentially a sign condition on s and the second term f belongs to $L^1(\Omega)$.

scholarly journals Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ge Dong ◽  
Xiaochun Fang
Keyword(s):  
Sobolev Spaces ◽  
Lower Order ◽  
Principal Part ◽  
Existence Of Solutions ◽  
Order Term ◽  
Convex Functional ◽  
Polynomial Type ◽  
Convex Functionals ◽  
Order Elliptic Operator ◽  
Lower Order Terms

We consider the existence of solutions of variational inequality form. Findu∈D(J):〈A(u),v-u〉+〈F(u),v-u〉+J(v)-J(u)≥0,∀v∈W1LM(Ω),whose principal part is having a growth not necessarily of polynomial type, whereAis a second-order elliptic operator of Leray-Lions type,Fis a multivalued lower order term, andJis a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces.

scholarly journals Existence of Solutions to Elliptic Problem with Convection Term and Lower-Order Term

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaohua He ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Yonglin Xu
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Order Term ◽  
Combined Effects ◽  
Convection Term ◽  
Bounded Smooth Domain ◽  
Bounded Smooth ◽  
Lower Order Terms

In this paper, we establish the existence of solutions to the following noncoercivity Dirichlet problem − div M x ∇ u + u p − 1 u = − div u E x + f x , x ∈ Ω , u x = 0 , x ∈ ∂ Ω , where Ω ⊂ ℝ N N > 2 is a bounded smooth domain with 0 ∈ Ω , f belongs to the Lebesgue space L m Ω with m ≥ 1 , p > 0 . The main innovation point of this paper is the combined effects of the convection terms and lower-order terms in elliptic equations.

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.

scholarly journals Strongly nonlinear elliptic variational unilateral problems in Orlicz space

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
L. Aharouch ◽  
A. Benkirane ◽  
M. Rhoudaf
Keyword(s):  
Existence Result ◽  
Order Term ◽  
Natural Growth ◽  
Unilateral Problem ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Carathéodory Function ◽  
Unilateral Problems ◽  
The Right

We will be concerned with the existence result of unilateral problem associated to the equations of the formAu+g(x,u,∇u)=f, whereAis a Leray-Lions operator from its domainD(A)⊂W01LM(Ω)intoW−1EM¯(Ω). On the nonlinear lower order termg(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to|∇u|, and satisfies the sign condition. The right-hand sidefbelongs toW−1EM¯(Ω).

scholarly journals Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces

2021 ◽  
Vol 55 (1) ◽  
pp. 43-70
Author(s):  
Abdeslam Talha ◽  
Mohamed Saad Bouh Elemine Vall
Keyword(s):  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Growth Conditions ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Unilateral Problems ◽  
Sign Conditions ◽  
Lower Order Terms

In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.

scholarly journals Strongly nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces

2014 ◽  
Vol 33 (1) ◽  
pp. 191 ◽  
Author(s):  
Mohamed Leimne Ahmed Oubeid ◽  
A. Benkirane ◽  
M. Sidi El Vally
Keyword(s):  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic

We prove in this paper the existence of solutions of strongly nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces. An approximation and a compactness results in inhomogeneous Musielak-Orlicz-Sobolev spaces have also been provided.

scholarly journals Quasilinear degenerate elliptic unilateral problems

2005 ◽  
Vol 2005 (1) ◽  
pp. 11-31 ◽  
Author(s):  
L. Aharouch ◽  
Y. Akdim ◽  
E. Azroul
Keyword(s):  
Lower Order ◽  
Existence Result ◽  
Order Term ◽  
Natural Growth ◽  
Unilateral Problem ◽  
Sign Condition ◽  
Carathéodory Function ◽  
Degenerate Elliptic ◽  
Unilateral Problems ◽  
The Right

We will be concerned with the existence result of a degenerate elliptic unilateral problem of the formAu+H(x,u,∇u)=f, whereAis a Leray-Lions operator fromW1,p(Ω,w)into its dual. On the nonlinear lower-order termH(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to|∇u|, but without assuming the sign condition. The right-hand sidefbelongs toL1(Ω).

scholarly journals Nonlinear elliptic equations with variable exponents involving singular nonlinearity

2021 ◽  
Vol 8 (4) ◽  
pp. 705-715
Author(s):  
H. Khelifi ◽  
◽  
Y. El Hadfi ◽  
◽  
Keyword(s):  
Sobolev Spaces ◽  
Lower Order ◽  
Elliptic Equations ◽  
Order Term ◽  
Nonlinear Elliptic Equations ◽  
Variable Exponents ◽  
Singular Nonlinearity ◽  
Nonlinear Elliptic ◽  
Regularizing Effects ◽  
Lower Order Terms

In this paper, we prove the existence and regularity of weak positive solutions for a class of nonlinear elliptic equations with a singular nonlinearity, lower order terms and L1 datum in the setting of Sobolev spaces with variable exponents. We will prove that the lower order term has some regularizing effects on the solutions. This work generalizes some results given in [1–3].

scholarly journals Nonlinear evolution problems with singular coefficients in the lower order terms

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Lower Order ◽  
Time Horizon ◽  
Existence Result ◽  
Nonlinear Evolution ◽  
Order Term ◽  
Time Behavior ◽  
Infinite Time ◽  
Singular Coefficient ◽  
Singular Coefficients ◽  
Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

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