Fourth order weighted elliptic problem under exponential nonlinear growth

2022/01/24 by Dridi, Brahim, Jaidane, Rached
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.09858

Abstract

We deal with nonlinear weighted biharmonic problem in the unit ball of ℝ⁴. The weight is of logarithm type. The nonlinearity is critical in view of Adam's inequalities in the weighted Sobolev space W^2,2₀(B,w). We prove the existence of non trivial solutions via the critical point theory. The main difficulty is the loss of compactness due to the critical exponential growth of the nonlinear term f. We give a new growth condition and we point out its importance for checking the Palais-Smale compactness condition.

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