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Zeitschrift für Analysis und ihre Anwendungen


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Volume 26, Issue 3, 2007, pp. 303–312
DOI: 10.4171/ZAA/1325

Published online: 2007-09-30

Existence Results for Strongly Nonlinear Elliptic Equations of Infinite Order

A. Benkirane[1], Moussa Chrif[2] and Said El Manouni[3]

(1) Université Sidi Mohamed Ben Abdellah, Fès, Morocco
(2) Université Moulay Ismail, Meknès, Morocco
(3) Al Imam University (IMSIU), Riyadh, Saudi Arabia

In this work, generalized Sobolev spaces and Sobolev spaces of infinite order are considered. Existence of solutions for strongly nonlinear equation of infinite order of the form $Au+g(x,u)=f$ is established. Here $A$ is an elliptic operator from a functional space of Sobolev type to its dual and $g(x,s)$ is a lower order term satisfying a sign condition on $s.$

Keywords: Strongly nonlinear elliptic equations of infinite order, monotonicity condition, sign condition

Benkirane A., Chrif Moussa, El Manouni Said: Existence Results for Strongly Nonlinear Elliptic Equations of Infinite Order. Z. Anal. Anwend. 26 (2007), 303-312. doi: 10.4171/ZAA/1325