Infinitely many solutions for double hamonic perturbed problem
Copyright policy )Infinitely many solutions for double hamonic perturbed problem
The author proves the existence of infinitely many nontrivial solutions of the problem \[ \Delta^2 u- a\Delta u+ bu= g(x, u)+ f(x, u)\text{ in }\Omega,\;u= \partial u/\partial n= 0\text{ on }\partial\Omega, \] under several growth conditions on \(g\) and \(f\), for \(a\geq 0\), \(b\geq 0\). The proof uses variational methods and index theories on Banach manifolds.
Boundary value problems for higher-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, semilinear elliptic equation of fourth order, Morse index
Boundary value problems for higher-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, semilinear elliptic equation of fourth order, Morse index
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