In this paper, we consider the existence and multiplicity of signchanging solutions to some Kirchhoff-type equation involving a nonlinear term with exponential growth. In a first result, we prove the existence of at least three solutions: one solution is positive, one is negative and the third one is sign-changing. The existence of infinitely many sign-changing solutions is proved as our second result in this work. Our method is mainly based on invariant sets of descending flow in the framework of classical critical point theory.
In this paper, we establish a new singular Trudinger–Moser type inequality for radial Sobolev spaces with logarithmic weights.
The existence of nontrivial solutions is proved for an elliptic equation defined in {\mathbb{R}^{n}}, relying on variational methods and involving a nonlinearity with doubly exponential growth at infinity.
In this paper, we establish some Adams' type inequality for weighted second-order Sobolev spaces in four dimensions. The weights are radial and can have a singular or decaying behavior. This inequality is used to study some nonhomogeneous quasilinear elliptic equation. Keywords Adams' inequality • Singular or decaying weights • Radial functions • Nonhomogeneous quasilinear elliptic equation • Exponential critical growth Mathematics Subject Classification 35A23 • 35B33 • 35J30 • 35J35 • 35J91 N −1 , |∇u| N is the Dirichlet norm, that is, |∇u| N := |∇u| N dx 1 N and ω N −1 is the measure of the unit sphere in R N. In addition, for any bounded domain , the supremum in (1.1) can be attained. This result has been generalized and extended in many B Sami Aouaoui
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.