On singular, functional, nonsmooth and implicit phi-Laplacian initial and boundary value problems

Functional fractional boundary value problems with singular ϕ-Laplacian

This paper discusses the existence of solutions of the fractional differential equations D(φ(Du)) = Fu, D(φ(Du)) = f(t, u, Du) satisfying the boundary conditions u(0) = A(u), u(T ) = B(u). Here μ, α ∈ (0, 1], ν ∈ (0, α], D is the Caputo fractional derivative, φ ∈ C(−a, a) (a > 0), F is a continuous operator, A,B are bounded and continuous functionals and f ∈ C([0, T ] × R). The existence result...

Positive and dead core solutions of singular Dirichlet boundary value problems with phi-Laplacian

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet boundary value problem (φ(u)) = λ[ f (t, u, u) + h(t, u, u)], u(0) = u(T ) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and h may be singular at the value 0 of its second phase variable. c © 2007 Elsevier L...

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

Boundary Value Problems with Singular Boundary Conditions

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions properties of the spectrum are studied and the completeness of the system of root functions is proved.

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.