We prove the existence of multiple positive radial solutions to a sign-indefinite elliptic boundary blow-up problem where the nonlinearity is a function superlinear at zero and at infinity and is multiplied by a sign changing weight function. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function. The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions is also considered.
Multiple positive solutions to elliptic boundary blow-up problems / Boscaggin, Alberto; Dambrosio, Walter; Papini, Duccio. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 262:12(2017), pp. 5990-6017. [10.1016/j.jde.2017.02.025]
Multiple positive solutions to elliptic boundary blow-up problems
PAPINI, Duccio
2017
Abstract
We prove the existence of multiple positive radial solutions to a sign-indefinite elliptic boundary blow-up problem where the nonlinearity is a function superlinear at zero and at infinity and is multiplied by a sign changing weight function. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function. The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions is also considered.File | Dimensione | Formato | |
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