On some fourth-order semilinear elliptic problems in R N

The existence of two solutions for a fourth-order semilinear elliptic problem involving critical growth from the viewpoint of Sobolev embedding was established. The basic tools used in the analysis were the mountain-pass theorem, constrained minimization, and concentration-compactness principle. The existence of positive principle eigenvalues for the corresponding linear elliptic problem was also investigated.

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