Existence and Multiplicity Results for Nonlinear Elliptic Problems in ℝN with an Indefinite Functional
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We prove the existence of a nontrivial solution for the nonlinear elliptic problem -∆u = λh(x)u + α(x)g(u) in ℝN, where g is superlinear near zero and near infinity, α(x) changes sign, λ is positive, and h(x) ≥ 0 is a weight function. For g odd, we prove the existence of an infinite number of solutions.
CitationCosta, D. G., Guo, Y., & Ramos, M. (2002). Existence and multiplicity results for nonlinear elliptic problems in RN with an indefinite functional. Electronic Journal of Differential Equations, 2002(25), pp. 1-15.
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