1 results
GROUND STATE SOLUTIONS FOR
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$-SUPERLINEAR 
$p$-LAPLACIAN EQUATIONS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 97 / Issue 1 / August 2014
- Published online by Cambridge University Press:
- 15 May 2014, pp. 48-62
- Print publication:
- August 2014
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- Article
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- You have access
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In this paper, we deduce new conditions for the existence of ground state solutions for the
$p$-Laplacian equation which weaken the Ambrosetti–Rabinowitz type condition and the monotonicity condition for the function
$$\begin{equation*} \left \{ \begin{array}{@{}ll} -\mathrm {div}(|\nabla u|^{p-2}\nabla u)+V(x)|u|^{p-2}u=f(x, u), \quad x\in {\mathbb {R}}^{N},\\[5pt] u\in W^{1, p}({\mathbb {R}}^{N}), \end{array} \right . \end{equation*}$$
$t\mapsto f(x, t)/|t|^{p-1}$. In particular, both 
$tf(x, t)$ and 
$tf(x, t)-pF(x, t)$ are allowed to be sign-changing in our assumptions.
