Ayazoglu, Rabil; Akkoyunlu, Ebubekir; Naghizadeh, Zohreh

We consider an initial boundary value problem for a class of anisotropic parabolic Ni-Serrin type equations with nonstandard nonlinearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. Because the nonlinear perturbation leads to difficulties (it does not have a definite sign) in obtaining a priori estimates in the energy method, we had to modify the Tartar method significantly. Under suitable assumptions, we obtain the global existence, decay and extinction of solutions.

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Ayazoglu (Mashiyev), R.; Alisoy, Gulizar

In this paper, we study the existence of infinitely many solutions for a class of stationary Schrödinger type equations in ℝN involving the p(x)-Laplacian. The non-linearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. The main arguments are based on the geometry supplied by Fountain Theorem. We also establish a Bartsch type compact embedding theorem for variable exponent spaces.

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