Ordinary p-Laplacian systems with nonlinear boundary conditions

Ordinary Differential Equations with Nonlinear Boundary Conditions

The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems. 2000 Mathematics Subject Classification: 34A45, 34B15, 34A40.

THE FIRST EIGENVALUE OF p-LAPLACIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions

We study the following p-Laplacian equation with nonlinear boundary conditions: -Δ(p)u + μ(x)|u|(p-2)u = f(x,u) + g(x,u),x ∈ Ω, | ∇u|(p-2)∂u/∂n = η|u|(p-2)u and x ∈ ∂Ω, where Ω is a bounded domain in ℝ(N) with smooth boundary ∂Ω. We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and f, g do not need to satisfy the (P.S) or (P.S...

Boundary value problems for nonlinear fractional differential equations with integral and ordinary-fractional flux boundary conditions

In this paper, we consider a new class of boundary value problems of Caputo type fractional differential equations supplemented with classical/nonlocal Riemann-Liouville integral and flux boundary conditions and obtain some existence results for the given problems. The flux boundary condition x′(0) = b cDβx(1) states that the ordinary flux x′(0) at the left-end point of the interval [0, 1] is p...

PERIODIC BOUNDARY VALUE PROBLEMS FOR nTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN

We prove existence results for solutions of periodic boundary value problems concerning the nth-order differential equation with p-Laplacian [φ(x(n−1)(t))]′ = f (t,x(t),x′(t), . . . , x(n−1)(t)) and the boundary value conditions x(i)(0)=x(i)(T), i= 0, . . . ,n− 1. Our method is based upon the coincidence degree theory of Mawhin. It is interesting that f may be a polynomial and the degree of som...