Existence and multiplicity of solutions for Kirchhoff-type potential systems with variable critical growth exponent. Issue 4 (4th March 2023) - Chems Eddine, Nabil
Abstract : In this paper, by using the concentration-compactness principle of Lions for variable exponents found in [Bonder JF, Silva A. Concentration-compactness principal for variable exponent space and applications. Electron J Differ Equ. 2010;141:1–18.] and the Mountain Pass Theorem without the Palais–Smale condition given in [Rabinowitz PH. Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math., Vol. 65, Amer. Math. Soc., Providence, RI, 1986.], we obtain the existence and multiplicity solutions u = ( u 1, u 2, … . u n ), for a class of Kirchhoff-Type Potential Systems with critical exponent, namely 1 − M i ( A i ( u i ) ) div ( B i ( ∇ u i ) ) = | u i | s i ( x ) − 2 u i + λ F u i ( x, u ) in Ω