Four versus two solutions of semilinear elliptic boundary value problems

Liu, Zhaoli; Sun, Jiwei

doi:10.1007/s005260100104

Cited by 9 publications

(2 citation statements)

References 4 publications

(3 reference statements)

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“…For example, it usually permits more flexible requirements on the growth condition of f and can also give some order properties of the solutions. For the applications of the sub-supersolution method to the semilinear and quasilinear elliptic problems, we refer to [3,4,[6][7][8][9][10]12,21,22,26,29] and the references therein. The goal of this paper is to study the subsupersolution method for (1.1), which is a new research topic.…”

Section: Consider the P(x)-laplacian Dirichlet Problemmentioning

confidence: 99%

On the sub-supersolution method for p(x)-Laplacian equations

Fan

2007

Journal of Mathematical Analysis and Applications

141

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This paper deals with the sub-supersolution method for the p(x)-Laplacian equations. A sub-supersolution principle for the Dirichlet problems involving the p(x)-Laplacian is established. It is proved that the local minimizers in the C 1 topology are also local minimizers in the W 1,p(x) topology for given energy functionals. A strong comparison theorem for the p(x)-Laplacian equations is presented. Some applications of the abstract theorems obtained in this paper to the eigenvalue problems for the p(x)-Laplacian equations are given.

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Section: Consider the P(x)-laplacian Dirichlet Problemmentioning

confidence: 99%

On the sub-supersolution method for p(x)-Laplacian equations

Fan

2007

Journal of Mathematical Analysis and Applications

141

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“…With the help of invariant sets in C 1 0 (Ω), sign-changing solutions were obtained in Refs. [11,31,33,[37][38][39][40][45][46][47]56] for semilinear elliptic equations on a bounded domain, in Refs. [41,44] for semilinear elliptic eigenvalue problems with constraints on a bounded domain, in Refs.…”

Section: Introductionmentioning

confidence: 99%