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

One-dimensional nonlinear boundary value problems with variable exponent

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Infinitely many solutions for a class of quasilinear two-point boundary value systems

The existence of infinitely many solutions for a class of Dirichlet quasilinear elliptic systems is established. The approach is based on variational methods

Existence results for a quasi-linear differential problem

The aim of this paper is to establish the existence of at least one non-trivial solution for Neumann quasi-linear problems. Our approach is based on variational methods

Gradient estimates for the perfect conductivity problem in anisotropic media

We study the perfect conductivity problem when two perfectly conducting inclusions are closely located to each other in an anisotropic background medium. We establish optimal upper and lower gradient bounds for the solution in any dimension which characterize the singular behavior of the electric field as the distance between the inclusions goes to zero

Stress concentration for closely located inclusions in nonlinear perfect conductivity problems

We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium Ω⊂RN, N≥2. The governing equation may be degenerate of p-Laplace type, with 1<p≤N. We prove optimal L∞ estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero

Infinitely many solutions for a perturbed p-Laplacian boundary value problem with impulsive effects

In this paper, we deal with the existence of weak solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. More precisely, the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods

Infinitely many solutions to boundary value problem for fractional differential equations

Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result

One-dimensional nonlinear boundary value problems with variable exponent

In this paper, a class of nonlinear differential boundary value problems with variable exponent is investigated. The existence of at least one non-zero solution is established, without assuming on the nonlinear term any condition either at zero or at infinity. The approach is developed within the framework of the Orlicz-Sobolev spaces with variable exponent and it is based on a local minimum theorem for differentiable functions