On a boundary value problem in the half-space

Liu, Xiangqing; Liu, Jiaquan

doi:10.1016/j.jde.2010.11.001

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Definition 12 ([26]1

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Cited by 11 publications

(1 citation statement)

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“…Remark 1.1 Theorem 5.1 in [26] tells us that the (PS) condition can be substituted by the weaker (C) condition in Lemma 1.2.…”

Section: Definition 12 ([26]mentioning

confidence: 99%

Multiple solutions of fourth-order difference equations with different boundary conditions

Wang

Chen

2019

Bound Value Probl

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In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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“…Remark 1.1 Theorem 5.1 in [26] tells us that the (PS) condition can be substituted by the weaker (C) condition in Lemma 1.2.…”

Section: Definition 12 ([26]mentioning

confidence: 99%

Multiple solutions of fourth-order difference equations with different boundary conditions

Wang

Chen

2019

Bound Value Probl

View full text Add to dashboard Cite

show abstract

Asymptotic behavior of least energy solutions for a singularly perturbed problem with nonlinear boundary condition

Abreu

Medeiros

2013

Calc. Var.

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Sign-Changing Solutions for Discrete Second-Order Periodic Boundary Value Problems

Zhou

et al. 2014

Bull. Malays. Math. Sci. Soc.

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On a boundary value problem in the half-space

Abstract: In this paper, we study the existence of positive solutions and signchanging solutions for the following boundary value problem in the half-spacewhere λ is a positive parameter and the nonlinear term f is superlinear at zero and asymptotically linear at infinity.

Cited by 11 publications

References 25 publications

Multiple solutions of fourth-order difference equations with different boundary conditions

Multiple solutions of fourth-order difference equations with different boundary conditions

Asymptotic behavior of least energy solutions for a singularly perturbed problem with nonlinear boundary condition

Sign-Changing Solutions for Discrete Second-Order Periodic Boundary Value Problems

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