An existence theorem of positive solutions to a singular nonlinear boundary value problem

summary:In this note we consider the boundary value problem $y''=f(x,y,y')$ $\,(x\in [0,X];X>0)$, $y(0)=0$, $y(X)=a>0$; where $f$ is a real function which may be singular at $y=0$. We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O'Regan [J. Differential Equations 84 (1990), 228–251]

Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities

AbstractMultiple critical points theorems for non-differentiable functionals are established. Applications both to elliptic variational–hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

Multiplicity Results for a Perturbed Elliptic Neumann Problem

The existence of three solutions for elliptic Neumann problems with a perturbed nonlinear term depending on two real parameters is investigated. Our approach is based on variational methods

Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

Abstract The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions

Existence results for a two point boundary value problem involving a fourth-order equation

We study the existence of non-zero solutions for a fourth-order differential equation with nonlinear boundary conditions which models beams on elastic foundations. The approach is based on variational methods. Some applications are illustrated

One-dimensional nonlinear boundary value problems with variable exponent

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Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

In this paper, a nonlinear differential problem involving the $p$-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results