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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.

##### MSC:
 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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