The presence of lower and upper solutions to semilinear elliptic equations is linked to some variational properties of the associated action functionals. We exploit this variational characterization to find existence and multiplicity of solutions when multiple lower and upper solutions are given in various ordering relations
Conti, M., Merizzi, L., Terracini, S. (1999). Remarks on variational methods and lower-upper solutions. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 6(4), 371-393 [10.1007/s000300050009].
Remarks on variational methods and lower-upper solutions
Terracini, S
1999
Abstract
The presence of lower and upper solutions to semilinear elliptic equations is linked to some variational properties of the associated action functionals. We exploit this variational characterization to find existence and multiplicity of solutions when multiple lower and upper solutions are given in various ordering relations
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