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This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…

Optimization and Control · Mathematics 2016-07-21 Xiaojun Lu , David Yang Gao

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…

Classical Analysis and ODEs · Mathematics 2007-05-23 Leszek Gasinski , Nikolaos S. Papageorgiou

We consider a class of double phase variational integrals driven by nonhomogeneous potentials. We study the associated Euler equation and we highlight the existence of two different Rayleigh quotients. One of them is in relationship with…

Analysis of PDEs · Mathematics 2018-10-19 Matija Cencelj , Vicenţiu D. Rădulescu , Dušan D. Repovš

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…

Analysis of PDEs · Mathematics 2017-03-16 Luca Scarpa

In this paper, we focus on (no)existence and asymptotic behavior of solutions for the double critical Maxwell equation involving with the Hardy, Hardy-Sobolev, Sobolev critical exponents. The existence and noexistence of solutions…

Analysis of PDEs · Mathematics 2024-11-22 Cong Wang , Jiabao Su

Combining monotonicity theory related to the parametric version of the Browder-Minty Theorem with fixed point arguments we obtain hybrid existence results for a system of two operator equations. Applications are given to a system of…

Analysis of PDEs · Mathematics 2023-08-16 Michał Bełdziński , Marek Galewski , Igor Kossowski

The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…

Analysis of PDEs · Mathematics 2016-04-04 Said El Manouni , Hichem Hajaiej , Patrick Winkert

In this paper, we study a class of double phase systems which contain the singular and mixed nonlinear terms. Unlike the single equation, the mixed nonlinear terms make the problem more complicate. The geometry of the fibering mapping has…

Analysis of PDEs · Mathematics 2025-03-27 Zhanbing Bai , Yizhe Feng

We consider two classes of nonlinear eigenvalue problems with double-phase energy and lack of compactness. We establish existence and non-existence results and related properties of solutions. Our analysis combines variational methods with…

Analysis of PDEs · Mathematics 2019-06-24 István Faragó , Dušan Repovš

In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…

Analysis of PDEs · Mathematics 2018-01-09 Abdelkader Lakmeche , Horiya Habbaze , Ahmed Lakmeche

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…

Numerical Analysis · Mathematics 2015-03-13 Burak Aksoylu , Michael L. Parks

In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such…

Analysis of PDEs · Mathematics 2023-08-22 Ángel Crespo-Blanco , Patrick Winkert

In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-Yosida operator. By using this variation of constants…

Dynamical Systems · Mathematics 2016-08-26 Pierre Magal , Ousmane Seydi

In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.

Classical Analysis and ODEs · Mathematics 2014-05-21 Marek Galewski , Ewa Schmeidel

In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…

Analysis of PDEs · Mathematics 2019-10-28 Leszek Gasinski , Patrick Winkert

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…

Classical Analysis and ODEs · Mathematics 2018-11-16 Lucía López-Somoza , Feliz Minhós

We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…

Mathematical Physics · Physics 2020-03-16 Michael Herrmann , Karsten Matthies

Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared…

Analysis of PDEs · Mathematics 2023-08-15 Hoang Hai Ha , Ky Ho

In this paper, we study a new class of mixed double phase problems that combine local and nonlocal operators. We consider two different models. The first model is driven by the fractional $p$-Laplacian together with a local double phase…

Analysis of PDEs · Mathematics 2026-05-26 Anupma Arora , Shilpa Gupta , Patrick Winkert

In this note a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one-dimensional fractional problems admits at least one non-trivial solution under an asymptotical behaviour of the…

Classical Analysis and ODEs · Mathematics 2014-02-10 Marek Galewski , Giovanni Molica Bisci