Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators

Jongrak Lee; Yun Ho Kim

doi:10.1186/s13661-016-0603-x

Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators

Jongrak Lee, Yun Ho Kim

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations (Formula presented.) Here the function φ(x, v) is of type | v| ^p ⁻ ²v and the functions f, g satisfy a Carathéodory condition. To do this, we give some critical point theorems for continuously differentiable functions with the Cerami condition which are extensions of the recent results in Bonanno (Adv. Nonlinear Anal. 1:205-220, 2012) and Bonanno and Marano (Appl. Anal. 89:1-10, 2010) by applying Zhong’s Ekeland variational principle.

Original language	English
Article number	95
Journal	Boundary Value Problems
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1186/s13661-016-0603-x
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Cerami condition
multiple critical points
p-Laplace type operator
weak solutions

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10.1186/s13661-016-0603-x

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title = "Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators",

abstract = "We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations (Formula presented.) Here the function φ(x, v) is of type | v| p − 2v and the functions f, g satisfy a Carath{\'e}odory condition. To do this, we give some critical point theorems for continuously differentiable functions with the Cerami condition which are extensions of the recent results in Bonanno (Adv. Nonlinear Anal. 1:205-220, 2012) and Bonanno and Marano (Appl. Anal. 89:1-10, 2010) by applying Zhong{\textquoteright}s Ekeland variational principle.",

keywords = "Cerami condition, multiple critical points, p-Laplace type operator, weak solutions",

author = "Jongrak Lee and Kim, \{Yun Ho\}",

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year = "2016",

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AU - Lee, Jongrak

AU - Kim, Yun Ho

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations (Formula presented.) Here the function φ(x, v) is of type | v| p − 2v and the functions f, g satisfy a Carathéodory condition. To do this, we give some critical point theorems for continuously differentiable functions with the Cerami condition which are extensions of the recent results in Bonanno (Adv. Nonlinear Anal. 1:205-220, 2012) and Bonanno and Marano (Appl. Anal. 89:1-10, 2010) by applying Zhong’s Ekeland variational principle.

AB - We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations (Formula presented.) Here the function φ(x, v) is of type | v| p − 2v and the functions f, g satisfy a Carathéodory condition. To do this, we give some critical point theorems for continuously differentiable functions with the Cerami condition which are extensions of the recent results in Bonanno (Adv. Nonlinear Anal. 1:205-220, 2012) and Bonanno and Marano (Appl. Anal. 89:1-10, 2010) by applying Zhong’s Ekeland variational principle.

KW - Cerami condition

KW - multiple critical points

KW - p-Laplace type operator

KW - weak solutions

UR - https://www.scopus.com/pages/publications/84971537755

U2 - 10.1186/s13661-016-0603-x

DO - 10.1186/s13661-016-0603-x

M3 - Article

AN - SCOPUS:84971537755

SN - 1687-2762

VL - 2016

JO - Boundary Value Problems

JF - Boundary Value Problems

IS - 1

M1 - 95

ER -

Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators

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Keywords

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