Multiplicity of solutions for a singular p-laplacian elliptic equation

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 a positive solution for a p-Laplacian equation with‎ ‎singular nonlinearities

‎In this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-Laplacian oprator and singular nonlinearities‎. ‎We‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ We find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎We use the method ...

Solutions for singular p-Laplacian equation in Rn

Existence and multiplicity of solutions for a Neumann-type p(x)-Laplacian equation with nonsmooth potential

In this paper we study Neumann-type p(x)-Laplacian equation with nonsmooth potential. Firstly, applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W (Ω). Finally, we obtain the existence of at least two nontrivial solutions, when α− > p.

Exact multiplicity of positive solutions for a p-Laplacian equation with positive convex nonlinearity

A p-Laplacian nonlinear elliptic equation with positive and p-superlinear nonlinearity and Dirichlet boundary condition is considered. We first prove the existence of two positive solutions when the spatial domain is symmetric or strictly convex by using a priori estimates and topological degree theory. For the ball domain in RN with N ≥ 4 and the case that 1 < p < 2, we prove that the equation...