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On superlinear $$p(x)$$-Laplacian equations in $$\mathbb R^N$$. (English) Zbl 1194.35142
Summary: We consider the $$p(x)$$-Laplacian equations in $$\mathbb R^N$$. The nonlinearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. We obtain ground states of the equations, improving a recent result of X. Fan [J. Math. Anal. Appl. 341, No. 1, 103–119 (2008; Zbl 1135.35034)]. We also establish a Bartsch-Wang type compact embedding theorem for variable exponent spaces. Then, a multiplicity result for the equations is proved for odd nonlinearity.

##### MSC:
 35J60 Nonlinear elliptic equations 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 35J20 Variational methods for second-order elliptic equations 35J70 Degenerate elliptic equations
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