We consider positive solutions to the non-variational family of equations
where , b(x) is a given function, g is an increasing nonlinearity with g(0)> 0 and is a bounded smooth domain. We introduce the definition of stability for non-variational problems and establish existence and regularity results for stable solutions. These results generalize the classical results obtained when is a constant function making the problem variational after a suitable transformation.
Submitted July 30, 2015. Published July 21, 2016.
Math Subject Classifications: 35B35, 35J61.
Key Words: Non-variational problem; stable solution.
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| Joana Terra |
Departamento de Matemática, FCEyN
and IMAS-CONICET, UBA (1428)
Buenos Aires, Argentina
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