Mathematics – Analysis of PDEs
Scientific paper
2012-03-15
Mathematics
Analysis of PDEs
Scientific paper
In this paper, we shall establish a Dancer-type unilateral global bifurcation result for a class of quasilinear elliptic problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that $(\mu_k^\nu(p),0)$ is a bifurcation point of the above problems and there are two distinct unbounded continua, $(\mathcal{C}_{k}^\nu)^+$ and $(\mathcal{C}_{k}^\nu)^-$, consisting of the bifurcation branch $\mathcal{C}_{k}^\nu$ from $(\mu_k^\nu(p), 0)$, where $\mu_k^\nu(p)$ is the $k$-th positive or negative eigenvalue of the linear problem corresponding to the above problems, $\nu\in\{+,-\}$. As the applications of the above unilateral global bifurcation result, we study the existence of nodal solutions for a class of quasilinear elliptic problems with sign-changing weight. Moreover, based on the bifurcation result of Dr\'{a}bek and Huang (1997) [\ref{DH}], we study the existence of one-sign solutions for a class of high dimensional quasilinear elliptic problems with sign-changing weight.
Dai Guowei
Ma Ruyun
No associations
LandOfFree
Unilateral global bifurcation and nodal solutions for the $p$-Laplacian with sign-changing weight does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Unilateral global bifurcation and nodal solutions for the $p$-Laplacian with sign-changing weight, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unilateral global bifurcation and nodal solutions for the $p$-Laplacian with sign-changing weight will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-30223