In this paper we are concerned with the existence and multiplicity of nodal solutions to the Dirichlet problem associated to the elliptic equation Δu + q(|x|)g(u) = 0 in the unit ball in R~N. The nonlinearity g has a linear growth at infinity and zero, while the weight function q is nonnegative in [0,1] and strictly positive in some interval [r_1,r_2] is contained in [0,1]. By means of a topological degree approach, we are able to prove the existence of solutions with prescribed nodal properties, depending on the behaviour of the ratio g(u)/u at infinity and zero.
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机译：在本文中，我们关注的是在R〜N的单位球中，与椭圆方程Δu+ q（| x |）g（u）= 0有关的Dirichlet问题的节点解的存在性和多重性。非线性g在无穷大和零处具有线性增长，而权重函数q在[0,1]中为非负值，在[0,1]中包含某个间隔[r_1，r_2]中严格为正。通过拓扑度方法，我们能够证明具有规定节点性质的解的存在，这取决于比g（u）/ u在无穷大和零时的行为。
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