The behavior of solutions of a parametric weighted $ (p, q) $-Laplacian equation

Large time behavior of solutions of the p-Laplacian equation

We establish the behavior of the solutions of the degenerate parabolic equation ut = ∇ · ( |∇u|∇u ) , p > 2, posed in the whole space with nonnegative, continuous and compactly supported initial data. We prove a nonlinear concavity estimate for the pressure v = u(p−2)/(p−1) away from the the maximum point of v. The estimate implies that the support of the solution becomes convex for large times...

The Method of Subsuper Solutions for Weighted p(r)-Laplacian Equation Boundary Value Problems

Existence of weak solutions for a class of (p,q)$(p,q)$-Laplacian systems

Multiplicity of solutions for a superlinear p-Laplacian equation

We consider quasi-linear elliptic equations involving the p-Laplacian with nonlinearities which interfere asymptotically with the spectrum of the differential operator. We show that such equations have for certain forcing terms at least two solutions. Such equations are of so-called Ambrosetti-Prodi type. In particular, our theorem is a partial generalization of corresponding results for the se...

Existence of solutions to a superlinear p - Laplacian equation ∗

Using Morse theory, we establish the existence of solutions to the equation −∆pu = f(x, u) with Dirichlet boundary conditions. We assume that ∫ s 0 f(x, t) dt lies between the first two eigenvalues of the p-Laplacian.