2009
DOI: 10.1016/j.jmaa.2008.12.053
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Multiple solutions for semilinear elliptic boundary value problems with double resonance

Abstract: In this paper we study the multiplicity of nontrivial solutions of semilinear elliptic boundary value problems which may be double resonance near infinity between two consecutive eigenvalues of − with zero Dirichlet boundary data. The methods we use here are Morse theory, minimax methods and bifurcation theory.

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Cited by 41 publications
(29 citation statements)
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“…The next result is useful in computing the critical groups at infinity. It is a slight generalization of a result of Perera and Schechter [17], suitable for functions ϕ ∈ C 1 (X) which satisfy the C-condition (see [12]). …”
Section: Introductionmentioning
confidence: 90%
“…The next result is useful in computing the critical groups at infinity. It is a slight generalization of a result of Perera and Schechter [17], suitable for functions ϕ ∈ C 1 (X) which satisfy the C-condition (see [12]). …”
Section: Introductionmentioning
confidence: 90%
“…As a consequence of these variational characterizations and of the unique continuation property, we have the following useful facts (see e.g., [10]). The next result, due to Liang and Su [22] (see also [18] for an extension to Banach spaces), is helpful in computing critical groups. It is a generalization of an earlier result of Perera and Schechter [32].…”
Section: Remark 23mentioning
confidence: 99%
“…Such problems have been studied extensively in the context of Dirichlet equations. In this direction, we mention the works of Costa and Silva [8], Hirano and Nishimura [14], Landesman et al [20], Liang and Su [22], Liu [24], Li and Su [25], Li and Zou [26], Su and Tang [34], Zou [37], and Zou and Liu [38]. For the corresponding Neumann problem, the bibliography is not that rich.…”
Section: Introductionmentioning
confidence: 99%
“…Such problems were investigated primarily in the context of Dirichlet equations. We mention the works of Hirano and Nishimura [1], Landesman et al [2], Liang-Su [3], Li-Willem [4], de Paiva [5], Su-Tang [6], and Zou [7]. The Neumann case has not been studied so extensively.…”
Section: Introductionmentioning
confidence: 99%