On nontrivial solutions of critical polyharmonic elliptic systems

Abstract

In the present work, we consider elliptic systems involving polyharmonic operators and critical exponents. We discuss the existence and nonexistence of nontrivial solutions to these systems. Our theorems improve and/or extend the ones established by Bartsch and Guo [T. Bartsch, Y. Guo, Existence and nonexistence results for critical growth polyharmonic elliptic systems, J. Differential Equations 220 (2006) 531-543] in both aspects of spectral interaction and regularity of lower order perturbations.

Existence and multiplicity results for critical growth polyharmonic elliptic systems

“…Recently, Bartsch and Guo established existence and nonexistence results for m , n ≥ 1 and F positively m 霴 ‐homogeneous. Subsequently, Montenegro extended the results in .…”

Nontrivial solutions for critical potential elliptic systems

“…Necessary and sufficient conditions for the existence of a nontrivial solution u of the system (3) have been discussed by various authors. In particular, Amster et al [1] and Bartsch and Guo [3] focused on the existence problem in the situation, closely related to (1), when G(t) = At, t , where A is a symmetric k × k matrix, and, more recently, Montenegro [22] addressed the problem for general potential functions G. Dealing with system (4), sufficient conditions for the existence of a positive weak solution u (i.e. a weak solution whose coordinates are nonnegative nonzero functions) have been established in the case k = 2 by De Morais Filho and Souto [12].…”

Multiplicity of Solutions for Biharmonic Elliptic Systems Involving Critical Nonlinearity

“…Thus it is necessary for us to investigate the critical biharmonic elliptic system (1.1) deeply. We also refer to more related systems, which can be seen in [2,8,14,15,16,17,20] and references therein.…”