The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1
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In this paper we study the asymptotic behavior of solutions to the (p,q)-equation [Formula presented]has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W01,q(Ω) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Ω) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions.
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1-laplacian, Asymptotic behavior, Functions of bounded variation, p goes to 1, Sign-changing solutions
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Inglês
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Nonlinear Analysis, Theory, Methods and Applications, v. 251.
