Infinitely many positive solutions for a p(x)-Kirchhoff-type equation
By Guowei Dai, Duchao Liu. 2009
81 citations recorded by the source corpus.
This paper is concerned with the existence of infinitely many positive solutions to a class of p(x)-Kirchhoff-type problem. By means of a direct variational approach and the theory of the variable exponent Sobolev spaces, we establish the existence of infinitely many distinct positive solutions whose W1,p(x)(Ω)-norms and L∞-norms tend to zero under suitable hypotheses about nonlinearity.
View Paper: https://www.semanticscholar.org/paper/235e59dd1649aaf7ae21c34a191050b1514c526a
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Citations in the corpus
- Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, methodology): “example, in [30], using variational methods, we have investigated nonlocal p(x)-Laplacian Dirichlet problem”
- Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities (2013, methodology): “In [11], the authors studied problem (1.”
- Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities (2012, methodology): “In [7], the authors studied problem (1.”
- Overview of differential equations with non-standard growth (2010, background): “After the completion of this paper, we learned that Liu, Qiu and Zhang [174, 177, 179] have partially generalized these to equations with ∆p(·) on the left hand side.”