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We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.
In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais–Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation , where are periodic in for and 0 is in a gap of the spectrum of ; . If for an appropriate constant , we show that this equation has a nontrivial solution.
In this paper we establish a variant
and generalized weak linking
theorem, which contains more delicate result and insures the existence of
bounded
Palais–Smale sequences of a strongly indefinite functional.
The abstract result will be used to study the
semilinear Schrödinger equation , where N ≥ 4; V,K,g are periodic
in xj for 1 ≤ j ≤ N and 0 is in a gap of the spectrum
of -Δ + V; K>0. If for an
appropriate constant c, we show that this equation has a
nontrivial solution.
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