Kristaly, A., Mezei, I.I. & Szilak, K. (2020) Nonlinear Analysis - Theory, Methods and Applications [Matematică, Q1]

Publicat: 06 Noiembrie 2020

Kristaly, A., Mezei, I.I. & Szilak, K. (2020) Differential inclusions involving oscillatory terms. Nonlinear Analysis - Theory, Methods and Applications, 197, 111834.

DOI: https://doi.org/10.1016/j.na.2020.111834

✓ Publisher: Elsevier
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics, Applied; Mathematics
✓ Article Influence Score (AIS): 1.142 (2020) / Q1 in all categories

Abstract: Motivated by mechanical problems where external forces are non-smooth, we consider the differential inclusion problem { -Delta u(x) is an element of partial derivative F(u(x)) + lambda partial derivative G(u(x)) in Omega; u >= 0, in Omega; (D-lambda) u = 0, on partial derivative Omega, where Omega subset of R-n is a bounded open domain, and partial derivative F and partial derivative G stand for the generalized gradients of the locally Lipschitz functions F and G. In this paper we provide a quite complete picture on the number of solutions of (D-lambda) whenever partial derivative F oscillates near the origin/infinity and partial derivative G is a generic perturbation of order p > 0 at the origin/infinity, respectively. Our results extend in several aspects those of Kristaly and Moro anu (2010).

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