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We establish several results related to existence, nonexistence or bifurcation of positive solutions for a Dirichlet boundary value problem with in a smooth bounded domain. The main feature of this paper consists in the presence of a…

Analysis of PDEs · Mathematics 2015-06-26 Marius Ghergu , Vicentiu Radulescu

It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the…

Analysis of PDEs · Mathematics 2024-02-20 Elves Alves de Barros e Silva , Sergio H. Monari Soares

In this article, we prove the existence of solutions to a nonlinear nonlocal elliptic problem with a singualrity and a discontinuous critical nonlinearity which is given as follows. \begin{align} \begin{split}\label{main_prob}…

Analysis of PDEs · Mathematics 2021-08-04 Kamel Saoudi , Akasmika Panda , Debajyoti Choudhuri

In this work, we study the existence of weak solution to the following quasi linear elliptic problem involving the fractional $p$-Laplacian operator, a Hardy potential and multiple critical Sobolev nonlinearities with singularities,…

Analysis of PDEs · Mathematics 2019-06-19 Ronaldo B. Assunção , Olímpio H. Miyagaki , Jeferson C. Silva

We prove the existence of one positive, one negative, and one sign-changing solution of a $p$-Laplacian equation on $\mathbb{R}^N$, with a $p$-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on…

Analysis of PDEs · Mathematics 2014-05-28 Ann Derlet , François Genoud

In this paper we consider a quasilinear singular anisotropic elliptic problem with a p-sublinear perturbation. We prove uniqueness of weak solutions and we provide necessary and sufficient conditions for the existence of weak solutions in…

Analysis of PDEs · Mathematics 2026-04-13 Francesco Esposito , Francescantonio Oliva , Eugenio Vecchi

In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…

Spectral Theory · Mathematics 2009-07-23 Nikolaos Papathanasiou , Panayiotis Psarrakos

The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying…

Analysis of PDEs · Mathematics 2023-09-15 Gurdev C. Anthal , Jacques Giacomoni , Konijeti Sreenadh

This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as $\e\to 0$, and the domain is…

Analysis of PDEs · Mathematics 2013-10-29 Riccardo Molle

In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation…

Functional Analysis · Mathematics 2015-06-23 Vladimir Strauss , Monika Winklmeier

In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for…

Analysis of PDEs · Mathematics 2019-06-03 Hana Didi , Brahim Khodja , Abdelkrim Moussaoui

This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak…

Analysis of PDEs · Mathematics 2026-02-17 Souvik Bhowmick , Sekhar Ghosh , Vishvesh Kumar

We study the existence of nontrivial weak solutions for a class of generalized $p(x)$-biharmonic equations with singular nonlinearity and Navier boundary condition. The proofs combine variational and topological arguments. The approach…

Analysis of PDEs · Mathematics 2020-05-06 Vicenţiu D. Rădulescu , Dušan D. Repovš

Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded…

Analysis of PDEs · Mathematics 2023-05-09 Debajyoti Choudhuri , Dušan D. Repovš , Kamel Saoudi

Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…

High Energy Physics - Phenomenology · Physics 2009-10-31 Wolfgang Lucha , F. F. Schoberl

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…

Analysis of PDEs · Mathematics 2025-02-27 Sanjit Biswas , Prashanta Garain

In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…

Analysis of PDEs · Mathematics 2020-11-18 Ricardo Lima Alves

We consider a Dirichlet elliptic problem driven by the Laplacian with singular and superlinear nonlinearities. The singular term appears on the left-hand side while the superlinear perturbation is parametric with parameter $\lambda>0$ and…

Analysis of PDEs · Mathematics 2019-09-12 Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu , Dušan D. Repovš

By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single-peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We…

Analysis of PDEs · Mathematics 2007-05-23 Marco Squassina

We study fourth-order quasilinear elliptic problems that involve the p-biharmonic operator and Navier boundary conditions. The nonlinear term grows at the critical Sobolev rate. Starting from a Hamiltonian system of two second-order…

Analysis of PDEs · Mathematics 2025-09-18 Kanishka Perera , Bruno Ribeiro