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In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li \cite{Li} combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.
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참고문헌 (33)
참고문헌 신청
Hajar Ansari / 2014 / Existence and multiplicity of solutions for fourth-order elliptic Kirchhoff equations with potential term / Complex Variables and Elliptic Equations 60(5):668~695
J.M Ball / 1973 / Initial-boundary value problems for an extensible beam / Journal of Mathematical Analysis and Applications 42(1):61~90
H. M. Berger / 1955 / A new approach to the analysis of large de ections of plates / J. Appl. Mech 22:465~472
Haim Brezis / 1983 / A Relation Between Pointwise Convergence of Functions and Convergence of Functionals / Proceedings of the American Mathematical Society 88(3):486~490
Alberto Cabada / 2014 / A generalization of an extensible beam equation with critical growth in RN / Nonlinear Analysis: Real World Applications 20:134~142
J.M Ball / 1973 / Initial-boundary value problems for an extensible beam / Journal of Mathematical Analysis and Applications 42(1):61~90
H. M. Berger / 1955 / A new approach to the analysis of large de ections of plates / J. Appl. Mech 22:465~472
Haim Brezis / 1983 / A Relation Between Pointwise Convergence of Functions and Convergence of Functionals / Proceedings of the American Mathematical Society 88(3):486~490
Alberto Cabada / 2014 / A generalization of an extensible beam equation with critical growth in RN / Nonlinear Analysis: Real World Applications 20:134~142
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