Remarks on Ricceri’s variational principle and applications to the p(x)-Laplacian equations

By Xianling Fan, Shao-Gao Deng. 2007

98 citations recorded by the source corpus.

Abstract In this paper we give some remarks on a variational principle of Ricceri in the case of sequentially weakly lower semi-continuous functionals defined on a reflexive real Banach space. In particular we introduce the notions of Ricceri block and Ricceri box which are more convenient in some applications than the weakly connected components. Using the variational principle of Ricceri and a local mountain pass lemma, we study the multiplicity of solutions of the p ( x ) -Laplacian equations with Neumann, Dirichlet or no-flux boundary condition, and under appropriate hypotheses, in which the integral functionals need not satisfy the ( PS ) condition on the global space, we prove that the problem has at least seven solutions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0d68358c03e053caf8f7416277d7b5aff4129564

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. P. Hasto
2. Petteri Harjulehto
3. Guowei Dai
4. Matti Nuortio
5. Ut V. Le
6. Abdelrachid El Amrouss
7. Anass Ourraoui
8. Vicentiu D. Rădulescu

In Computational Theory and Mathematics

1. P. Hasto
2. Petteri Harjulehto
3. Guowei Dai
4. Matti Nuortio
5. Ut V. Le
6. Abdelrachid El Amrouss
7. Anass Ourraoui
8. Vicentiu D. Rădulescu

In Mathematical Physics

1. P. Hasto
2. Petteri Harjulehto
3. Matti Nuortio
4. Ut V. Le
5. Anass Ourraoui
6. Guowei Dai
7. Jan Vyb'iral
8. H. Kempka

Citations in the corpus

• Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent (2014, unknown): “The problem (Dλ,f ) has been studied by several authors (see for instance [3–5,10,9,13,12,14,15,8,18,19, 19,20,22,26]).”
• Existence of solutions for a boundary problem involving p(x)-biharmonic operator (2012, background): “(see [6,8]) Assume that I, J : X → R are sequentially weakly lower semi continuous and G is a Ricceri block of I with type ρ.”
• Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, background): “In 37 , Fan and Deng established the version of the result of Ricceri for variables exponents.”
• Overview of differential equations with non-standard growth (2010, background): “Therefore we content ourselves with presenting the list of such papers: [64, 65, 66, 87, 90, 91, 93, 101, 102, 105, 106, 129, 130, 140, 149, 168, 176].”