Abstract
In this work, a biharmonic elliptic system is investigated in mathbb{R}^{N}, which involves singular potentials and multiple critical exponents. By the Rellich inequality and the symmetric criticality principle, the existence and multiplicity of G-invariant solutions to the system are established. To our best knowledge, our results are new even in the scalar cases.
Highlights
In this article, we study the singular fourth-order elliptic problem: ⎧ ⎪⎪⎨ = μ u |x|4 + Q(x) m i=1 ςi αi 2∗∗ |u|αi–2u|v|βi + σ h(x)|u|q–2u, ⎪⎪⎩
1 Introduction In this article, we study the singular fourth-order elliptic problem:
Elliptic systems involving the G-invariant solutions have seldom been studied; we only find a handful of results in [27,28,29,30]
Summary
By applying analytic techniques and critical point theory, several results on the existence and multiplicity of G-invariant solutions to (1.2) were obtained. (2) Problem (P0Q) has at least one nontrivial solution if lim|x|→∞ Q(x) = Q(∞) exists and is positive, Q(∞) ≥ max To establish the existence results for problem (P0Q), we need the following local (PS)c condition, which is indispensable for the proof of Theorem 2.1.
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