| Existence of one weak solution for $p(x)$-biharmonic equations involving a concave-convex nonlinearity |
| R.A. Mashiyev, G. Alisoy, I. Ekincioglu |
Abstract In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involving a $p(x)$-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained.
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Keywords: Critical points; $p(x)$-biharmonic operator; Navier boundary conditions; concave-convex nonlinearities; Mountain Pass Theorem; Ekeland's variational principle. |
MSC: 35J60, 35J48 |
Pages: 296$-$307 |
Volume 69 , Issue 4 , 2017 |
