科研之友
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摘要
We consider existence and multiplicity of sign-changing solutions for a class of quasilinear problems which has received considerable attention in the past, including the so called Modified Nonlinear Schrodinger Equations. We develop a new variational approach to treat this class of quasilinear equations by proposing a p-Laplacian regularization process. By establishing necessary estimates we show the solutions to the perturbation problems converge in a sense to solutions of the original problems. We show that the new approach is especially effective for dealing with issues of multiple solutions and sign-changing solutions.
