Gelfand-type problems involving the 1-Laplacian operator
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2022Resumen
This paper is concerned with the Gelfand problem for the p-Laplacian with p=1 and a strictly positive and increasing nonlinearity f. It is shown that there exists a sharp threshold λ∗, depending on the Cheeger constant of the domain, such that for λ<λ∗ the function u≡0 is a solution of the problem, which is somehow surprising since f(0)>0, while no solutions exist for λ>λ∗. The analysis of the many solutions found in the radial case allows the identification of bounded solutions, as well as the understanding of the limit as p→1 of solutions of the p-Laplace-Gelfand problem.
Palabra/s clave
Nonlinear elliptic equations
1-Laplacian operator
Gelfand problem