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Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

100%

Long Y., Zeng B.

Open Mathematics

2017

tom 15

nr 1

1549-1557

In this paper, we study second-order nonlinear discrete Robin boundary value problem with parameter dependence. Applying invariant sets of descending flow and variational methods, we establish some new sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions of the system when the parameter belongs to appropriate intervals. In addition, an example is given to illustrate our results.

Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

81%

Long Y., Zhang Y., Shi H.

Open Mathematics

2016

tom 14

nr 1

520-530

By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

Ograniczanie wyników

2 Open Mathematics

2 Long Y.

1 Shi H.

1 Zeng B.

1 Zhang Y.

1 2017

1 2016

Wyniki wyszukiwania

Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence

Homoclinic solutions of 2nth-order difference equations containing both advance and retardation