On a new class of elliptic systems with nonlinearities of arbitrary growth
- Kristály, Alexandru
DOIAbstract
AbstractWe guarantee the existence of infinitely many different pairs of solutions to the system{−Δu=vpin Ω;−Δv=f(u)in Ω;u=v=0on ∂Ω, where 0<p<2N−2, Ω is a bounded domain in RN and the continuous nonlinear term f has an unusual oscillatory behavior. The sequence of solutions tends to zero (resp., infinity) with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity (resp., at zero) whenever f oscillates near zero (resp., at infinity). Our results provide the first applications of Ricceri's variational principle in the theory of coupled elliptic systems
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