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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 ...
- Source :
- Journal of the Australian Mathematical Society; Aug2014, Vol. 97 Issue 1, p48-62, 15p
- Publication Year :
- 2014
-
Abstract
- In this paper, we deduce new conditions for the existence of ground state solutions for the $p$-Laplacian equation $$\begin{equation*} \left \{ \begin{array}{@{}ll} -\mathrm {div}(<INNOPIPE>\nabla u<INNOPIPE>^{p-2}\nabla u)+V(x)<INNOPIPE>u<INNOPIPE>^{p-2}u=f(x, u), \quad x\in {\mathbb {R}}^{N},\\[5pt] u\in W^{1, p}({\mathbb {R}}^{N}), \end{array} \right . \end{equation*}$$ which weaken the Ambrosetti–Rabinowitz type condition and the monotonicity condition for the function $t\mapsto f(x, t)/<INNOPIPE>t<INNOPIPE>^{p-1}$. In particular, both $tf(x, t)$ and $tf(x, t)-pF(x, t)$ are allowed to be sign-changing in our assumptions. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICAL functions
MATHEMATICAL analysis
EQUATIONS
MATHEMATICS
HYPOTHESIS
Subjects
Details
- Language :
- English
- ISSN :
- 14467887
- Volume :
- 97
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 97175139
- Full Text :
- https://doi.org/10.1017/S1446788714000135