Minimax Theory and its Applications 04 (2019), No. 1, 071--085
Copyright Heldermann Verlag 2019
Sequences of Weak Solutions for a Navier Problem Driven by the p(x)-Biharmonic Operator
Filippo Cammaroto
Dept. of Mathematical and Computer Sciences, University of Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
fdcammaroto@unime.it
Luca Vilasi
Dept. of Mathematical and Computer Sciences, University of Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
lvilasi@unime.it
We derive the existence of infinitely many solutions for an elliptic problem involving both the p(x)-biharmonic and the p(x)-Laplacian operators under Navier boundary conditions. Our approach is of variational nature and does not require any symmetry of the nonlinearities. Instead, a crucial role is played by suitable test functions in some variable exponent Sobolev space, of which we provide the abstract structure better suited to the framework.
Keywords: p(x)-biharmonic operator, p(x)-Laplacian operator, Navier problem, multiplicity.
MSC: 35J35, 35J60.
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