11 research outputs found
Existence of renormalized solutions for some degenerate and non-coercive elliptic equations
summary:This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by \begin{aligned}t 2&-{\rm div}( b(|u|)|\nabla u|^{p-2}\nabla u) + d(|u|)|\nabla u|^{p} = f - {\rm div}(c(x)|u|^{\alpha }) &\quad &\mbox {in}\ \Omega ,\\ & u = 0 &\quad &\mbox {on}\ \partial \Omega , \end{aligned}t where is a bounded open set of () with and under some growth conditions on the function and where is assumed to be in We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded
Existence of solutions in the sense of distributions of anisotropic nonlinear elliptic equations with variable exponent
The aim of this paper is to study the existence of solutions in the sense of distributions for a~strongly nonlinear elliptic problem where the second term of the equation is in which is the dual space of the anisotropic Sobolev and later will be in~
Parabolic problems in non-standard Sobolev spaces of infinite order
This paper is devoted to the study of the existence of solutions for the strongly nonlinear -parabolic equationwhere is a Leray-Lions operator acted from into its dual. The nonlinear term satisfies growth and sign conditions and the datum is assumed to be in the dual space $V^{-\infty,p'(x)}(a_\alpha,Q_{T})\>.
An existence result for two-dimensional parabolic integro-differential equations involving CEV model
In this paper, we present an existence result of weak solutions for some parabolic equations involving the so-called CEV model with jumps
Existence of infinitely many weak solutions for some quasilinear -elliptic Neumann problems
summary:We consider the following quasilinear Neumann boundary-value problem of the type We prove the existence of infinitely many weak solutions for our equation in the anisotropic variable exponent Sobolev spaces and we give some examples
Existence and regularity of entropy solutions for strongly nonlinear p(x)-elliptic equations
This article is devoted to study the existence of solutions for the strongly nonlinear p(x)-elliptic problem with and , also we will give some regularity results for these solutions
Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data
In this article, we study the following noncoercive quasilinear parabolic problem ∂u∂t−diva(x,t,u,∇u)+ν∣u∣s−1u=λ∣u∣p−2u∣x∣p+finQT,u=0onΣT,u(x,0)=u0inΩ,\left\{\begin{array}{ll}\frac{\partial u}{\partial t}-\hspace{0.1em}\text{div}\hspace{0.1em}a\left(x,t,u,\nabla u)+\nu {| u| }^{s-1}u=\lambda \frac{{| u| }^{p-2}u}{{| x| }^{p}}+f& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{Q}_{T},\\ u=0& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}{\Sigma }_{T},\\ u\left(x,0)={u}_{0}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\end{array}\right. with f∈L1(QT)f\in {L}^{1}\left({Q}_{T}) and u0∈L1(Ω){u}_{0}\in {L}^{1}\left(\Omega ) and show the existence of entropy solutions for this noncoercive parabolic problem with Hardy potential and L1-data
Existence of solutions for some quasilinear -elliptic problem with Hardy potential
summary:We consider the anisotropic quasilinear elliptic Dirichlet problem where is an open bounded subset of containing the origin. We show the existence of entropy solution for this equation where the data is assumed to be in and is a positive constant
Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data
In this paper, we study the existence of entropy solutions for some nonlinear elliptic equation of the type Au - \mbox{div }\phi(u) + H(x,u,\nabla u) = \mu, where is an operator of Leray-Lions type acting from into its dual, the strongly nonlinear term is assumed only to satisfy some nonstandard growth condition with respect to here and belongs to