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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