An Application of a Mountain Pass Theorem

Zhou, Huan Song

doi:10.1007/s101140100147

Cited by 21 publications

(18 citation statements)

References 12 publications

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“…Then, as a rule, σ cannot be taken constant. Furthermore, there is no need to assume F (x, t) ≥ 0 or that lim t→∞ t −1 f (x, t) is x-independent or bounded, two key ingredients in the approach to existence via the generic result of Jeanjean when p = 2 ([3], [7]). …”

Section: Introductionmentioning

confidence: 99%

Bounded Palais-Smale sequences for functionals with a mountain pass geometry

Rabier

2007

Arch. Math.

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We prove the existence of bounded Palais-Smale sequences for abstract functionals with a mountain pass geometry under hypotheses weaker than those commonly used in the literature. This is obtained via a generalization of a generic result of Jeanjean, combined with a rescaling argument. Applications to the existence of nontrivial solutions to semilinear elliptic problems are given. Mathematics Subject Classification (2000). 58E05, 58E30, 35J35.

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Section: Introductionmentioning

confidence: 99%

Bounded Palais-Smale sequences for functionals with a mountain pass geometry

Rabier

2007

Arch. Math.

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“…In this paper we extend a result obtained by Zhou in [27]. Here we are able to treat more general nonlinearities, and our main improvement consists in allowing g to change sign.…”

Section: The Functions α β Defined By (H3) (H4)(i) Are Clearly Measmentioning

confidence: 59%

“…Here we are able to treat more general nonlinearities, and our main improvement consists in allowing g to change sign. While in [27] the results are derived using a particular version of the Mountain Pass Theorem, in the present paper we are able to prove, using the classical Mountain Pass Theorem of Ambrosetti-Rabinowitz (see [5]), that problem (1.1) has always a positive solution under assumptions (H1) − (H4).…”

Section: The Functions α β Defined By (H3) (H4)(i) Are Clearly Measmentioning

confidence: 73%

A Dirichlet problem with asymptotically linear and changing sign nonlinearity

Lucia¹,

Magrone²,

Zhou³

2003

Rev. Mat. Complut.

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“…As f (x, t) ∈ C(Ω × R) is asymptotically linear, not super-linear, with respect to t at infinity, Zhou [8] researched the existence of positive solutions of problem (1.1) and obtained the following theorem.…”

Section: Introductionmentioning

confidence: 99%