Infinitely many solutions for nonlinear elliptic problems in the whole space

This paper investigates the existence of infinitely many weak solutions for a nonlinear elliptic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> </mml:math> -Laplacian equation defined in the whole space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mi>N</mml:mi> </mml:msup> </mml:math> . In particular, the equation is parameter-dependent and a range of positive parameters in which the equation admits such solutions is provided. Moreover, some particular cases in which the solutions turn out to be nonnegative are presented. The study is conducted via variational methods and critical points theory.