He, YuboTang, XianhuaZhang, Wen2022-03-212022-03-212017-01-16He, Y., Tang, X., & Zhang, W. (2017). Semiclassical solutions of perturbed biharmonic equations with critical nonlinearity. <i>Electronic Journal of Differential Equations, 2017</i>(19), pp. 1-15.1072-6691https://hdl.handle.net/10877/15524We consider the perturbed biharmonic equations ε4∆2u + V(x)u = ƒ(x, u), x ∈ ℝN and ε4∆2u + V(x)u = Q(x)|u|2**-2u + ƒ(x, u), x ∈ ℝN where ∆2 is the biharmonic operator, N ≥ 5, 2** = 2N/N-4 is the Sobolev critical exponent, Q(x) is a bounded positive function. Under some mild conditions on V and ƒ, we show that the above equations have at least one nontrivial solution provided that ε ≤ ε0, where the bound ε0 is formulated in terms of N, V, Q and ƒ.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalPerturbed biharmonic equationSemiclassical solutionCritical nonlinearityArticle