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Multiplicity results for \(p\)-biharmonic problems via Morse theory. (English) Zbl 1192.35042
The equation studied in this paper is the fourth order \(p\)-biharmonic problem \(\Delta_p^2u=f(x,u)\), where the right-hand side is assumed to have subcritical growth in \(u\). Using Morse theory, conditions are given under which the Dirichlet problem for this equation has at least one or even two nontrivial solutions.

MSC:
35J30 Higher-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
35J35 Variational methods for higher-order elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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