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

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.

Existence and regularity results for unilateral problems with degenerate coercivity

In this paper we prove some existence and regularity results for nonlinear unilateral problems with degenerate coercivity via the penalty method.

Existence results for diffusion–convection equations of nonlinear unilateral problems defined in Orlicz–Sobolev spaces

We prove the existence result of unilateral problems associated to strongly nonlinear elliptic equations whose model, including the diffusion–convection equation, is [Formula: see text]. We study exactly the following general case [Formula: see text] where [Formula: see text] is a Leray–Lions operator having a growth not necessarily of polynomial type, the lower order term [Formula: see text] : [Formula: see text] is a Carathéodory function, for a.e. [Formula: see text] and for all [Formula: see text] satisfying only a growth condition and the right-hand side [Formula: see text] belongs to [Formula: see text].

Existence of Solutions for Some Nonlinear Elliptic Anisotropic Unilateral Problems with Lower Order Terms

In this paper, we prove the existence of entropy solutions for anisotropic elliptic unilateral problem associated to the equations of the form$$ - \sum\limits_{i = 1}^N {{\partial _i}{a_i}(x,u,\nabla u) - } \sum\limits_{i = 1}^N {{\partial _i}{\phi _i}(u) = f,} $$where the right hand side f belongs to L1(Ω). The operator $- \sum\nolimits_{i = 1}^N {{\partial _i}{a_i}\left( {x,u,\nabla u} \right)} $ is a Leray-Lions anisotropic operator and ϕi ∈ C0(ℝ,ℝ).

Existence of entropy solutions for degenerate elliptic unilateral problems with variable exponents

In this article, we study the following degenerate unilateral problems: $$ -\mbox{ div} (a(x,\nabla u))+H(x,u,\nabla u)=f,$$ which is subject to the Weighted Sobolev spaces with variable exponent $W^{1,p(x)}_{0}(\Omega,\omega)$, where $\omega$ is a weight function on $\Omega$, ($\omega$ is a measurable, a.e. strictly positive function on $\Omega$ and satisfying some integrability conditions). The function $H(x,s,\xi)$ is a nonlinear term satisfying some growth condition but no sign condition and the right hand side $f\in L^1(\Omega)$.