Semiclassical solutions of perturbed biharmonic equations with critical nonlinearity
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We consider the perturbed biharmonic equations
ε4∆2u + V(x)u = ƒ(x, u), x ∈ ℝN
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.
CitationHe, Y., Tang, X., & Zhang, W. (2017). Semiclassical solutions of perturbed biharmonic equations with critical nonlinearity. Electronic Journal of Differential Equations, 2017(19), pp. 1-15.
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