Geodesic
Continuous dependence of solutions for indefinite semilinear elliptic problems
Electronic journal of differential equations, Tome 2013 (2013)
We consider the superlinear elliptic problem

$ -\Delta u + m(x)u = a(x)u^p $

in a bounded smooth domain under Neumann boundary conditions, where $m \in L^{\sigma}(\Omega), \sigma\geq N/2$ and $a\in C(\overline{\Omega})$ is a sign changing function. Assuming that the associated first eigenvalue of the operator $-\Delta + m $ is zero, we use constrained minimization methods to study the existence of a positive solution when $\widehat{m}$ is a suitable perturbation of m.
Classification : 35J20, 35J60, 35Q55
Keywords: positive solution, constrained minimization, eigenvalue problem, Neumann boundary condition, unique continuation 
@article{EJDE_2013__2013__a161,
     author = {Silva,  Elves A.B. and Silva,  Maxwell L.},
     title = {Continuous dependence of solutions for indefinite semilinear elliptic problems},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1291.35080},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a161/}
}
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AU  - Silva,  Maxwell L.
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JO  - Electronic journal of differential equations
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%A Silva,  Maxwell L.
%T Continuous dependence of solutions for indefinite semilinear elliptic problems
%J Electronic journal of differential equations
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%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a161/
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%F EJDE_2013__2013__a161
Silva,  Elves A.B.; Silva,  Maxwell L. Continuous dependence of solutions for indefinite semilinear elliptic problems. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a161/