We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at $+infty$ and sublinear at $-infty$. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.
Candito, P., Livrea, R., Papageorgiou, N. (2016). Nonlinear elliptic equations with asymmetric asymptotic behavior at $pminfty$. NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS, 32, 159-177 [10.1016/j.nonrwa.2016.04.005].
Nonlinear elliptic equations with asymmetric asymptotic behavior at $pminfty$
Livrea, Roberto;
2016-01-01
Abstract
We consider a nonlinear, nonhomogeneous Dirichlet problem with reaction which is asymptotically superlinear at $+infty$ and sublinear at $-infty$. Using minimax methods together with suitable truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions one of which is negative.
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