In this paper, we establish a unilateral global interval bifurcation result for the p-Laplacian equation. Furthermore, we shall prove the existence of the principal half-eigenvalues for the half-linear p-Laplacian equation. Moreover, we also investigate the existence of radial nodal solutions for the problems.
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where 1< p < +∞, ψp(s)=|s|p-2s, a(r) ∈ C[0, 1], a(r) ≥ 0,a(r)?0 on any subinterval of[0, 1]; λ is a parameter, u+=max{u, 0}, u-=-min{u,0}, α, β ∈ C[0, 1] are radially symmetric; f ∈ C(R, R), sf(s) > 0 for s∈R+, and f0 ∈[0, ∞) and f∞ ∈ (0, ∞) or f0 ∈ (0, ∞] and f∞=0 or f0=0 and f∞=∞, where f0=
f(s)/s, f∞=
f(s)/s. We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.
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