On a necessary condition in the calculus of variations in Orlicz-Sobolev spaces
Existence of solutions of strongly nonlinear elliptic equations in R.
The paper is dedicated to the existence of local solutions of strongly nonlinear equations in R and the Orlicz spaces framework is used.
Existence results for quasilinear degenerated equations via strong convergence of truncations.
In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x,u,∇u) = f, where A is a Leray-Lions operator from W (Ω,ω) into its dual, while g(x,s,ξ) is a nonlinear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. The right hand side f is assumed to belong either to W(Ω,ω*) or to L(Ω).
Existence of Solution for Quasilinear Degenerated Elliptic Unilateral Problems
An existence theorem is proved, for a quasilinear degenerated elliptic inequality involving nonlinear operators of the form , where is a Leray-Lions operator from into its dual, while is a nonlinear term which has a growth condition with respect to and no growth with respect to , but it satisfies a sign condition on , the second term belongs to .
Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz-Sobolev spaces
We discuss the existence of entropy solution for the strongly nonlinear unilateral parabolic inequalities associated to the nonlinear parabolic equations ∂u/∂t - div(a(x,t,u,∇u) + Φ(u)) + g(u)M(|∇u|) = μ in Q, in the framework of Orlicz-Sobolev spaces without any restriction on the N-function of the Orlicz spaces, where -div(a(x,t,u,∇u)) is a Leray-Lions operator and . The function g(u)M(|∇u|) is a nonlinear lower order term with natural growth with respect to |∇u|, without satisfying the sign...
An existence theorem for a strongly nonlinear elliptic problem in Musielak-Orlicz spaces
We prove an existence result for some class of strongly nonlinear elliptic problems in the Musielak-Orlicz spaces , under the assumption that the conjugate function of φ satisfies the Δ₂-condition.
Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data
We prove an existence result of entropy solutions for a class of strongly nonlinear parabolic problems in Musielak-Sobolev spaces, without using the sign condition on the nonlinearities and with measure data.
Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form
We prove the existence of solutions to nonlinear parabolic problems of the following type: where is a strictly increasing function of class , the term is an operator of Leray-Lions type which satisfies the classical Leray-Lions assumptions of Musielak type, is a Carathéodory, noncoercive function which satisfies the following condition: for all , where is the Musielak complementary function of , and the second term belongs to .
On the -regularity of solutions of nonlinear elliptic equations in Orlicz spaces.
Leray Lions degenerated problem with general growth condition.
Strongly nonlinear degenerated unilateral problems with data.
Strongly nonlinear degenerated elliptic unilateral problems via convergence of truncations.
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