Abstract
In the first part of this work, we recall variational methods related to invariant sets in \({C^1_0}\). In the second part of the work, we consider an elliptic Dirichlet problem in a situation where the origin is a solution around which the nonlinearity has a slope between two consecutive eigenvalues of order larger than 2 and near + infinity the slope of the nonlinearity is smaller than the first eigenvalue. Then we discuss the conditions needed near - infinity in order to ensure the existence of a positive solution and two sign-changing solutions.
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De Coster, C. Sign-changing solutions and multiplicity results for elliptic problems via lower and upper solutions. Nonlinear Differ. Equ. Appl. 16, 745 (2009). https://doi.org/10.1007/s00030-009-0033-x
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DOI: https://doi.org/10.1007/s00030-009-0033-x