Linking solutions for p-Laplace equations with nonlinear boundary conditions and indefinite weight

Existence of Solutions for Quasilinear Elliptic Equations with Nonlinear Boundary Conditions and Indefinite Weight

In this article, we establish the existence and non-existence of solutions for quasilinear equations with nonlinear boundary conditions and indefinite weight. Our proofs are based on variational methods and their geometrical features. In addition, we prove that all the weak solutions are in C1,β(Ω) for some β ∈ (0, 1).

MULTIPLE SOLUTIONS FOR THE p-LAPLACE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS

In this note, we show the existence of at least three nontrivial solutions to the quasilinear elliptic equation −∆pu + |u|p−2u = f(x, u) in a smooth bounded domain Ω of RN with nonlinear boundary conditions |∇u|p−2 ∂u ∂ν = g(x, u) on ∂Ω. The proof is based on variational arguments.

A Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear Dynamical Boundary Conditions

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

Bifurcation for positive solutions of nonlinear diffusive logistic equations in R with indefinite weight

We consider a diffusive p–logistic equation in the whole of R with absorption and an indefinite weight. Using variational and truncation techniques we prove a bifurcation theorem and describe completely the bifurcation point. In the semilinear case p = 2, under an additional hypothesis on the absorption term, we show that the positive solution is unique.