2018
DOI: 10.1002/mana.201700059
|View full text |Cite
|
Sign up to set email alerts
|

Existence and multiplicity of solutions for ‐Laplacian equations in

Abstract: In this paper, we study a class of sublinear or superlinear p(x)‐Laplacian equations in RN. Some new criteria to guarantee that the existence of multiple solutions for the considered problem is established by using the Morse theory and minimax methods.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

0
8
0

Year Published

2020
2020
2024
2024

Publication Types

Select...
6
1

Relationship

2
5

Authors

Journals

citations
Cited by 13 publications
(8 citation statements)
references
References 38 publications
0
8
0
Order By: Relevance
“…For almost twenty years, there have been some existence and multiplicity results for elliptic equations with this operator. The interested readers may refer to [1,2,14,23,27,28,32,34,39,40,45,51,54,55,57,58,60] and the references therein. For the study the regularity of solutions of p( • )-Laplacian equation, many results have been obtained [3, 6-9, 13, 15, 26, 35, 46, 56].…”
Section: Introduction and The Main Resultsmentioning
confidence: 99%
“…For almost twenty years, there have been some existence and multiplicity results for elliptic equations with this operator. The interested readers may refer to [1,2,14,23,27,28,32,34,39,40,45,51,54,55,57,58,60] and the references therein. For the study the regularity of solutions of p( • )-Laplacian equation, many results have been obtained [3, 6-9, 13, 15, 26, 35, 46, 56].…”
Section: Introduction and The Main Resultsmentioning
confidence: 99%
“…Moreover, using a variant of the Fountain theorem, Xie & Chen [13] also obtained the conclusion in [7] when the following assumptions hold: (C 2 ) VCfalse(double-struckRNfalse), V − > 0 and there exists a constant d 0 > 0 such that lim|y|false→+normal∞measfalsefalse{xdouble-struckRN:|xy|d0,Vfalse(xfalse)Mfalsefalse}=0, for all M>0. …”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…Motivated by all the facts mentioned above, it is very natural for us to pose the following questions: (Q 1 ) As we can see, the condition (C 1 ) in [7], or the condition (C 2 ) in [13], or the condition (C 3 ) in [9] is assumed to ensure that the required compact embedding theorem holds. Can one establish a suitable variational framework for problem (P) with no periodic or no radial symmetry?…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…Up to now, a large number of results have been obtained for solutions to equations related to this operator. For instance, we must mention the works of Kefi-Radulescu [9], Saoudi [10], Kefi-Saoudi [11], Xie-Chen [12], Nhan-Chuong-Truong [13], Zhang [14], Zhang-Motreanu [15], Yucedag [16], Yin-Li-Ke [17], Ait Hammou-Azroul-Lahmi [18], Ayazoglu-Ekincioglu [19], Ge-Wang [20], Ge-Lv [21], Ge-Radulescu [22], Heidarkhani-Afrouzi-Moradi-Caristi-Ge [23], Ge-Zhou-Wu [24], Fan [25] and the references therein. In relation to the regularity for solutions of differential equations with p(x)-Laplacian operator, we refer the readers to to [26][27][28][29][30][31][32][33][34][35][36], respectively, and the references therein.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%