Anisotropic nonlinear problem of infinite order with variables exponents and $L^1$ data
• Moussa Chrif,
• hakima ouyahya
Moussa Chrif
Université Moulay Ismail
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hakima ouyahya
Université Moulay Ismail Faculté des Sciences
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## Abstract

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 $L^1(\Omega)$.