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- W2971606177 abstract "We deal with existence and multiplicity results for the following nonhomogeneous and homogeneous equations, respectively: begin{eqnarray*} (P_g)quad - Delta_{lambda} u + V(x) u = f(x,u)+g(x),;mbox{ in } R^N,; end{eqnarray*} and begin{eqnarray*} (P_0)quad - Delta_{lambda} u + V(x) u = K(x)f(x,u),;mbox{ in } R^N,; end{eqnarray*} where $Delta_{lambda}$ is the strongly degenerate operator, $V(x)$ is allowed to be sign-changing, $Kin C(R^N,R)$, $g:R^NtoR$ is a perturbation and the nonlinearity $f(x,u)$ is a continuous function does not satisfy the Ambrosetti-Rabinowitz superquadratic condition ($(AR)$ for short). First, via the mountain pass theorem and the Ekeland's variational principle, existence of two different solutions for $(P_g)$ are obtained when $f$ satisfies superlinear growth condition. Moreover, we prove the existence of infinitely many solutions for $(P_0)$ if $f$ is odd in $u$ thanks an extension of Clark's theorem near the origin. So, our main results considerably improve results appearing in the literature." @default.
- W2971606177 created "2019-09-12" @default.
- W2971606177 creator A5047720995 @default.
- W2971606177 date "2019-09-08" @default.
- W2971606177 modified "2023-09-27" @default.
- W2971606177 title "Multiple solutions for Grushin operator without odd nonlinearity" @default.
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