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- Title
Unilateral Global Bifurcation, Half-Linear Eigenvalues and Constant Sign Solutions for a Fractional Laplace Problem.
- Authors
Yang, Bian-Xia; Sun, Hong-Rui; Feng, Zhaosheng
- Abstract
In this paper, we are concerned with the unilateral global bifurcation structure of fractional differential equation with nondifferentiable nonlinearity . It shows that there are two distinct unbounded subcontinua and consisting of the continuum emanating from , and two unbounded subcontinua and consisting of the continuum emanating from . As an application of this unilateral global bifurcation results, we present the existence of the principal half-eigenvalues of the half-linear fractional eigenvalue problem. Finally, we deal with the existence of constant sign solutions for a class of fractional nonlinear problems. Main results of this paper generalize the known results on classical Laplace operators to fractional Laplace operators.
- Subjects
BIFURCATION theory; NONDIFFERENTIABLE functions; NONLINEAR theories; EIGENVALUES; FRACTIONAL differential equations; LAPLACE'S equation
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2017, Vol 27, Issue 1, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127417500158