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Multiple positive solutions for quasilinear elliptic equations of \(p(x)\)-Laplacian type with sign-changing nonlinearity. (English) Zbl 1316.35138
There are established sufficient conditions for the existence of multiple positive solutions to nonautonomous quasilinear elliptic equations with \(p(x)\)-Laplacian and sign-changing nonlinearity \[ -\Delta_{p(x)}u=\lambda f(x,u)\quad x\in\Omega, \qquad u(x)=0\quad \partial \Omega. \] For solving the Dirichlet problem the authors use variational and topological methods. The nonexistence of positive solutions is also studied.

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J35 Variational methods for higher-order elliptic equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J40 Boundary value problems for higher-order elliptic equations
35B09 Positive solutions to PDEs
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