Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian

On the Existence of Solutions for Impulsive Fractional Differential Equations

“…In addition, since Rabinowitz established unilateral global bifurcation theorems, there have been many researches in global bifurcation theory and it has been applied to obtain the existence and multiplicity for solutions of differential equations (see, for instance, [8][9][10][11][12][13][14][15][16] and their references). However, the previous researches seldom involve both global bifurcation techniques and fractional differential equations.…”

Bifurcation from infinity and nodal solutions of quasilinear problems without the signum condition

“…However, as pointed out by Dancer [5,6] and López-Gómez [7], the proofs of these theorems contain gaps. Fortunately, Dancer [5] gave a corrected version of the unilateral global bifurcation theorem for a linear operator which has been extended to the one-dimensional p-Laplacian problem by Dai and Ma [8]. Moreover, Dai and Ma [8] also considered the existence of nodal solutions for the one-dimensional p-Laplacian 0-Dirichlet problem with the signum condition.…”

“…Fortunately, Dancer [5] gave a corrected version of the unilateral global bifurcation theorem for a linear operator which has been extended to the one-dimensional p-Laplacian problem by Dai and Ma [8]. Moreover, Dai and Ma [8] also considered the existence of nodal solutions for the one-dimensional p-Laplacian 0-Dirichlet problem with the signum condition. In [9], Ambrosetti and Hess studied the global behavior of the components of positive solutions of Dirichlet problems of asymptotically linear elliptic equations without the signum condition.…”

Positive convex solutions of boundary value problems arising from Monge–Ampère equations

“…h Remark 7.1. For the related results on the global behavior of positive solutions of diverse boundary value problems, see [24][25][26] and references therein.…”