Related papers: Existence and multiplicity of solutions for double…

In this work, we study the existence and multiplicity of solutions for a class of problems involving the $\phi$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational…

In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…

We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation $-\Delta u = (1-u) u^m - \lambda u^n$ in a bounded domain $\Omega \subset…

We consider a nonlinear Robin problem driven by the $p$-Laplacian plus an indefinite potential. The reaction term is of arbitrary growth and only conditions near zero are imposed. Using critical point theory together with suitable…

We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We…

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…

We prove a Br\'ezis--Oswald type existence theorem for positive solutions of semilinear equations in an abstract setting in which the underlying linear operator has a compact positivity-improving resolvent. The assumptions imposed on the…

We study sharp conditions for the existence and nonexistence of infinitely many nonnegative solutions to the problem $-\Delta_p u = \lambda f(u)$ in a bounded domain with Dirichlet boundary conditions, where $f$ is a continuous function…

Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…

This paper is concerned with the existence and uniqueness of the solution to a doubly nonlinear parabolic problem which arises directly from a circuit model of microwave heating. Beyond the relevance from a physical point of view, the…

By applying Ricceri's variational principle, we demonstrate the existence of solutions for the following Robin problem \begin{equation*}\left\{ \begin{array}{cc}-\func{div}\left( \omega _{1}(x)\left\vert \nabla u\right\vert^{p(x)-2}\nabla…

We use a variational approach to study existence and regularity of solutions for a Neumann $p$-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Trace theorems…

In this paper, we study the existence and multiplicity of weak solutions to a general type of Kirchhoff equations in magnetic fractional Orlicz-Sobolev spaces. Specifically, we appeal to Critical Point Theory to prove the existence of…

In this paper we prove the existence of multiple solutions for a quasilinear elliptic boundary value problem, when the p-derivative at zero and the p-derivative at infinity of the nonlinearity are greater than the first eigenvalue of the…

We establish Ambrosetti -Prodi type results for periodic solutions of one -dimensional nonlinear problems with drift term and drift -less whose principal operator is the fractional Laplacian of order $s\in(0,1)$. We establish conditions for…

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(\phi_1,\phi_2)$-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we…

This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on…

We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…

We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive…

We prove the existence of infinitely many classical periodic solutions for a class of semilinear wave equations with periodic boundary conditions. Our argument relies on some new estimates for the linear problem with periodic boundary…