The research is financed by the Natural Science Foundation of China and the National Natural Science Foundation of Neimongo. No. 10661008 and 200711020102 (Sponsoring information) Abstract In this paper, we consider an indefinite Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In an appropriate space K, we define a new self-adjoint operato...

This article concerns the critical fractional p-Laplacian equation with indefinite weights $$ (-\Delta_p)^su=\lambda g(x)|u|^{p-2}u+h(x)|u|^{p_s^*-2}u \quad \text{in }\mathbb{R}^N, where \(0<s<1<p<\infty\), \(N>sp\) and \(p_s^*=Np/(N-sp)\), weight functions \(g\) may be indefinite, \(h\) changes sign. Specifically, based on results of asymptotic estimates for an extremal in Sobol...

We prove the existence of at least three weak solutions for fourth-order problem with indefinite weight involving Leray–Lions operator nonstandard growth conditions. The proof our main result uses variational methods and critical theorem Bonanno Marano [Appl. Anal. 89 (2010) 1–10].

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained 2-block convex composite optimization problems with each block in the objective being the sum of a non-smooth convex function (p(x) or q(y)) and a smooth convex function (f(x) or g(y)), i.e., minx∈X , y∈Y{p(x) + f(x) + q(y) + g(y) | A∗x + B∗y = c}. B...

We prove the existence of infinitely many sign changing radial solutions for a \begin{document}$ p $\end{document}-Laplacian Dirichlet problem in ball. Our involves weight function that is positive at center unit ball and negative its boundary. Standard initial value problems-phase plane analysis argument...