Elliptic equations with indefinite concave nonlinearities near the origin

Abstract

In this note existence of infinitely many solutions is proved for an elliptic equation with indefinite concave nonlinearities.

A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractionalp(⋅)-Laplacian

“…As far as we are aware, there were no such regularity and existence results for fractional p(·)-Laplacian problems. In comparison with the papers [5,8,20], the main difficulty to obtain our second aim is to show the L ∞ -bound of weak solutions for the given problem. We remark that the strategy for obtaining this multiplicity is to assign a regularity-type result in our second aim.…”

Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN

“…This theorem is also not applicable if we drop the condition on nonlinear term f (·, t) at infinity and the oddness of f globally. To overcome this difficulty, the authors of [24,38,[41][42][43][44] employed the modified functional method and global variational formulation. In this regard, our attempt is new because we utilize the dual-fountain theorem in place of global variational formulation to obtain our main result.…”

“…The condition on nonlinear term f (·, t) at infinity, and the oddness of f globally is essential in applying this theorem. However, by employing the dual-fountain theorem, we design our main theorem when f (·, t) is carried out near zero, and f (·, t) is odd in t for a small t. Therefore, our approach for obtaining this consequence is somewhat different from former related works [8,9,24,29,38,[41][42][43][44].…”

Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators

“…Wang [28], utilizes the modified functional method and global variational formulation in [29] as the main tools. We also refer to the papers [28,[30][31][32][33][34][35]. However, we design our consequence under a different approach from the previous works.…”