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In this paper, we study the existence of positive solutions to the $p$-Kirchhoff elliptic equation involving general subcritical growth $$ (a+\lambda\int_{\mathbb{R}^N}|\nabla u|^p dx+\lambda b\int_{\mathbb{R}^N}|u|^p dx)(-\Delta_p u+b|u|^{p-2}u)=h(u),\ \mbox{in}\ \mathbb{R}^N, $$ where $a,\ b>0$, ${\lambda}$ is a parameter and the nonlinearity $h(s)$ satisfies the weaker conditions than the ones in our known literature. We also consider the asymptotics of solutions with respect to the parameter $\lambda$.
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참고문헌 (21)
참고문헌 신청
C. Alves / 2005 / Positive solutions for a quasilinear elliptic equation of Kirchhoff type / Comput. Math. Appl 49 (1) : 85 ~ 93
C. Chen / 2013 / Multiple solutions to the nonhomogeneous p-Kirchhoff elliptic equation with concave-convex nonlinearities / Appl. Math. Lett 36 (7) : 754 ~ 759
C. Chen / 2014 / Existence of positive solutions to p-Kirchhoff type-problem without compactness conditions / Appl. Math. Lett 28 : 82 ~ 87
G. Autuori / 2014 / On the existence of stationary solutions for higher-order p-Kirchhoff problems / Commun. Contemp. Math 16 (5) : 1 ~ 43
G. Kirchhoff / 1983 / Mechanik / Teubner
C. Chen / 2013 / Multiple solutions to the nonhomogeneous p-Kirchhoff elliptic equation with concave-convex nonlinearities / Appl. Math. Lett 36 (7) : 754 ~ 759
C. Chen / 2014 / Existence of positive solutions to p-Kirchhoff type-problem without compactness conditions / Appl. Math. Lett 28 : 82 ~ 87
G. Autuori / 2014 / On the existence of stationary solutions for higher-order p-Kirchhoff problems / Commun. Contemp. Math 16 (5) : 1 ~ 43
G. Kirchhoff / 1983 / Mechanik / Teubner
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