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We consider the p(x)-Laplacian equations in RN . The potential function does not satisfy the coercive condition. We obtain the existence of infinitely many solutions of the equations, improving a recent result of Duan–Huang [L. Duan, L. H. Huang, Electron. J. Qual. Theory Differ. Equ. 2014, No. 28, 1–13].

electronic journal on the qualitative theory of differential equations

Infinitely many solutions for elliptic problems in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msup></mml:math>involving the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Laplacian

Infinitely many solutions for elliptic problems inRNinvolving thep(x)-Laplacian