On nodal solutions for nonlinear elliptic equations with a nonhomogeneous differential operator

He, Tian-Xiao; Yan, Hongming; Sun, Zhaohong; Zhang, Meng

doi:10.1016/j.na.2015.02.002

Cited by 8 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If f (x, •) is odd, Theorem 4.1 gives a whole sequence {u n } ⊆ C 1 (Ω) of nodal solutions to (1.1) such that u n → 0 in C 1 (Ω). The works [9,14] contain similar results concerning Dirichlet problems without indefinite potential. All of them exploit an abstract theorem by Kajikiya [11].…”

Section: Introductionmentioning

confidence: 76%

Multiple nodal solutions to a Robin problem with sign-changing potential and locally defined reaction

Guarnotta

Marano

Papageorgiou

2019

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

View full text Add to dashboard Cite

A Robin boundary-value problem with non-homogeneous differential operator, indefinite potential, and reaction defined only near zero is investigated. The existence of one or more nodal solutions is achieved by using truncation, perturbation, and comparison techniques, results from Morse theory, besides variational methods.Let (X, · ) be a real Banach space. Given a set V ⊆ X, write V for the closure of V , ∂V for the boundary of V , and int X (V ) or simply int(V ), when no confusion can arise, for the interior of V . If x ∈ X and δ > 0 then B δ (x) := {z ∈ X : z − x < δ} , B δ := B δ (0) .

show abstract

Section: Introductionmentioning

confidence: 76%

Multiple nodal solutions to a Robin problem with sign-changing potential and locally defined reaction

Guarnotta

Marano

Papageorgiou

2019

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

View full text Add to dashboard Cite

show abstract

“…Boundary value problems with a combination of several differential operators of different nature (in particular, as in (GEV ; α, β)) arise mainly as mathematical models of physical processes and phenomena, and have been extensively studied in the last two decades, see, e.g., [15,30,19,13] and the references below. Among the historically first examples one can mention the Cahn-Hilliard equation [12] describing the process of separation of binary alloys, and the Zakharov equation [33, (1.8)] which describes the behavior of plasma oscillations.…”

Section: Introductionmentioning

confidence: 99%

On sign-changing solutions for (p,q)-Laplace equations with two parameters

Bobkov

Tanaka

2016

Advances in Nonlinear Analysis

View full text Add to dashboard Cite

We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for a two-parametric family of partially homogeneous (p, q)-Laplace equations −∆ p u−∆ q u = α|u| p−2 u+ β|u| q−2 u where p = q. By virtue of the Nehari manifolds, the linking theorem, and descending flow, we explicitly characterize subsets of the (α, β)-plane which correspond to the existence of nodal solutions. In each subset the obtained solutions have prescribed signs of energy and, in some cases, exactly two nodal domains. The nonexistence of nodal solutions is also studied. Additionally, we explore several relations between eigenvalues and eigenfunctions of the p-and q-Laplacians in one dimension.

show abstract

Nonlinear Nonhomogeneous Elliptic Problems

Papageorgiou¹,

Vetro²,

Vetro

2019

Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

View full text Add to dashboard Cite

the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

show abstract

On nodal solutions for nonlinear elliptic equations with a nonhomogeneous differential operator

Cited by 8 publications

References 30 publications

Multiple nodal solutions to a Robin problem with sign-changing potential and locally defined reaction

Multiple nodal solutions to a Robin problem with sign-changing potential and locally defined reaction

On sign-changing solutions for (p,q)-Laplace equations with two parameters

Nonlinear Nonhomogeneous Elliptic Problems

Contact Info

Product

Resources

About