Bifurcation for the $p$-Laplacian in ${\bf R}^N$
Jesús García Azorero, Eugenio Montefusco, Ireneo Peral · Advances in Differential Equations · 2000
In this work we look for positive (weak) solutions of the following problemswith 1 < p < ∞, 1 < q < p < r < p * , whereλ is a real parameter, α ≥ 0, h and g verify some integrability conditions.When p = 2 the problem corresponds to the classical Laplacian and also in this case the results are new.We will study three different cases: (I) The case where α = 1, h ∈ L s (R N ), for all s ∈ (1, ∞], and g ∈ L t (R N ), where t is an exponent that will be made precise later.We look for solutions u ∈ W 1,p (R N ).