Geodesic
Continuous dependence of solutions for indefinite semilinear elliptic problems
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a61,
     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},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a61/}
}
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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__a61/