P Value Problems

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Efficient p-value estimation in massively parallel testing problems

We present a new method to efficiently estimate very large numbers of p-values using empirically constructed null distributions of a test statistic. The need to evaluate a very large number of p-values is increasingly common with modern genomic data, and when interaction effects are of interest, the number of tests can easily run into billions. When the asymptotic distribution is not easily ava...

EIGENVALUE CHARACTERIZATION FOR (n; p) BOUNDARY-VALUE PROBLEMS

We consider the .n; p/ boundary value problem y C 1⁄2H .t; y/ D 1⁄2K .t; y/; n 1⁄2 2; t 2 .0; 1/; y.1/ D y.0/ D 0; 0 i n 2; where 1⁄2 > 0 and 0 p n 1 is fixed. We characterize the values of 1⁄2 such that the boundary value problem has a positive solution. For the special case 1⁄2 D 1, we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

In this article, we study a class of boundary value problems with p-Laplacian. By using a “Green-like” functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are ...