The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent

Ching-Yu, Chen; Wu, Tsung‐fang

doi:10.1016/j.amc.2012.04.026

Cited by 21 publications

(11 citation statements)

References 26 publications

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“…Nowadays scientists and researchers paid more attentions to problem (E 2 ) with sighchanging weight function. For instance, the case α + β = 2 * is considered in [13], whereas in [14,15] the case α + β < 2 * was studied, and the existence and multiplicity of positive solutions when (λ, μ) belongs to a certain subset of R 2 were obtained.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities

Lou

Qin

2020

Adv Differ Equ

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We consider the combined effect of concave-convex nonlinearities on the number of solutions for an indefinite truncated Kirchhoff-type system involving the weight functions. When α + β < 4, since the concave-convex nonlinearities do not satisfy the mountain pass geometry, it is difficult to obtain a bounded Palais-Smale sequence by the usual mountain pass theorem. To overcome the problem, we properly introduce a method of Nehari manifold and then establish the existence of multiple positive solutions when the pair of the parameters is under a certain range.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities

Lou

Qin

2020

Adv Differ Equ

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“…More naturally, it can be the populations by the competing species in . Therefore, there have been many papers concerned with the existence and multiplicity of positive solutions for problems related to ( E f , g ), for instance, and their references.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight

Fan

Liu

2014

Math Methods in App Sciences

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Communicated by S. ChenIn this paper, we study the multiplicity results of positive solutions for a semi-linear elliptic system involving critical growth terms. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we investigate how the coefficient h.x/ of the critical nonlinearity affects the number of positive solutions of that problem and get a relationship between the number of positive solutions and the topology of the global maximum set of h.

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“…In both the articles they have shown that the systems have at least two solutions. Many authors have tried to address problems on system of equations (see, for example, [3,29,11,4,32,30,8]).…”

Section: Introductionmentioning

confidence: 99%

A System of p-Laplacian Equations on the Sierpinski Gasket

Sahu¹,

Priyadarshi²

2018

Preprint

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In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpiński gasket in R 2 . Parameters λ, γ, α, β are real and 1 < q < p < α + β. Functions a, b, h : S → R are suitably chosen. For p > 1 we show the existence of at least two nontrivial weak solutions to the system of equations for some (λ,for all (φ 1 , φ 2 ) ∈ dom 0 (E p ) × dom 0 (E p ), then we will call (u, v) to be a weak solution of (1.1). Differential equation on fractal domains has been of great interest for researcher for past few decades. We will go back in time line and give a brief review of literature survey. In [18,19,26,12], Laplacian is defined

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The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent

Cited by 21 publications

References 26 publications

Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities

Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities

Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight

A System of p-Laplacian Equations on the Sierpinski Gasket

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