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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.
In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces.
We present a Furi-Pera type theorem for weakly sequentially continuous maps. As an application we establish new existence principles for elliptic Dirichlet problems.
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