Nonlinear elliptic equations with variable exponent: old and new

From MaRDI portal
Publication:2349496

DOI10.1016/j.na.2014.11.007zbMath1321.35030OpenAlexW2056623216MaRDI QIDQ2349496

Vicenţiu D. Rădulescu

Publication date: 22 June 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.11.007




Related Items (only showing first 100 items - show all)

A Hardy-Littlewood-Sobolev-type inequality for variable exponents and applications to quasilinear Choquard equations involving variable exponentGeneralized Choquard equations driven by nonhomogeneous operatorsExistence of solutions for Kirchhoff type problems in Musielak-Orlicz-Sobolev spacesNehari type ground state solutions for periodic Schrödinger–Poisson systems with variable growthOn the Steklov problem involving the p(x)-Laplacian with indefinite weightSolutions to p(x)-Laplace type equations via nonvariational techniquesUnnamed ItemDouble Phase Implicit Obstacle Problems with Convection and Multivalued Mixed Boundary Value ConditionsImproved bounds for solutions of ϕ-LaplaciansInfinitely many solutions for anisotropic variable exponent problemsA weighted eigenvalue problems driven by both \(p(\cdot)\)-harmonic and \(p(\cdot)\)-biharmonic operatorsOn the fourth-order Leray–Lions problem with indefinite weight and nonstandard growth conditionsUnnamed ItemUnnamed ItemOn sufficient ``local conditions for existence results to generalized \(p(.)\)-Laplace equations involving critical growthThe well-posedness problem of an anisotropic porous medium equation with a convection termOn some equation defined on the whole euclidean space ℝN and involving the p(u)‐LaplacianExistence of three weak solutions for fourth-order Leray–Lions problem with indefinite weightsMultiple solutions for a class of generalized critical noncooperative Schrödinger systems in \(\mathbb{R}^N\)Regularity theory for non-autonomous problems with a priori assumptionsThree solutions to mixed boundary value problem driven by p(z)‐Laplace operatorThe fundamental solution and blow-up problem of an anisotropic parabolic equationAn \(L^1\)-theory for a nonlinear temporal periodic problem involving \(p(x)\)-growth structure with a strong dependence on gradientsNodal solutions for a supercritical problem with variable exponent and logarithmic nonlinearityPeriodic solutions for a degenerate double-phase parabolic equation with variable growthUnnamed ItemExistence and multiplicity results for anisotropic double-phase differential inclusion with unbalanced growth and lack of compactnessMultiplicity results for a system involving the p(x)- Laplacian operatorNonnegative nontrivial solutions for a class of \(p(x)\)-Kirchhoff equation involving concave-convex nonlinearitiesAn existence result to some local and nonlocal \(p(u)\)-Laplacian problem defined on \({\mathbb{R}}^N\)Uniqueness and stability analysis to a system of nonlocal partial differential equations related to an epidemic modelExistence of solutions for a critical Choquard-Kirchhoff problem with variable exponentsThe Neumann problem for a class of generalized Kirchhoff-type potential systemsMultiplicity of solutions for a nonhomogeneous problem involving a potential in Orlicz-Sobolev spacesLower semicontinuity and relaxation for free discontinuity functionals with non-standard growthSolutions of the mean curvature equation with the Nehari manifoldAn eigenvalue problem for a variable exponent problem, via topological degreeExistence and regularity of solutions for a class of singular (p(x), q(x))-Laplacian systemsExistence and nonexistence of solutions for p(x)-curl systems arising in electromagnetismUnnamed ItemGround state solutions and multiple solutions for ap(x)-Laplacian equation in with periodic dataDouble phase transonic flow problems with variable growth: nonlinear patterns and stationary wavesDouble-phase problems and a discontinuity property of the spectrumAsymptotic properties of a $\varphi$-Laplacian and Rayleigh quotientON SOLVABILITY OF A CLASS OF NONLINEAR ELLIPTIC TYPE EQUATION WITH VARIABLE EXPONENTUnnamed ItemUnnamed ItemExistence results for Steklov problem involving thep(x)-Laplace operatorOn quasilinear elliptic problems without the Ambrosetti-Rabinowitz conditionExistence of solutions for a p(x)-biharmonic problem under Neumann boundary conditionsExistence of Solutions for Some Quasilinear Degenerate Elliptic Inclusions in Weighted Sobolev SpacesNonhomogeneousp(x)-Laplacian Steklov problem with weightsExistence result for a gradient-type elliptic system involving a pair ofp(x) andq(x)-Laplacian operatorsA new class of nonhomogeneous differential operator and applications to anisotropic systemsMultiplicity results forp(x)-biharmonic equations with Navier boundary conditionsUnnamed ItemAnisotropic problem with non-local boundary conditions and measure dataIsotropic and anisotropic double-phase problems: old and newRemarks on eigenvalue problems for fractional p ( · )-LaplacianMulti-bump solutions for quasilinear elliptic equations with variable exponents and critical growth in ℝNUnnamed ItemINFINITELY MANY LOW- AND HIGH-ENERGY SOLUTIONS FOR A CLASS OF ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTThe Dirichlet problem for nonlinear elliptic equations with variable exponentInfinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearityMaximal regularity for local minimizers of non-autonomous functionalsBlow-up of solutions to a viscoelastic parabolic equation with positive initial energySolving the singular two-dimensional fourth order problem by the mortar spectral element methodMultiplicity results involving \(p\)-biharmonic Kirchhoff-type problemsExact multiplicity of solutions for discrete second order Neumann boundary value problemsInfinitely many solutions for Neumann problems associated to non-homogeneous differential operators through Orlicz-Sobolev spacesDouble phase problems with variable growthDifferential equations of divergence form in separable Musielak-Orlicz-Sobolev spacesCombined effects of concave-convex nonlinearities in a fourth-order problem with variable exponentOn the existence of infinite sequences of ordered positive solutions of nonlinear elliptic eigenvalue problemsInfinitely many solutions for a nonlinear difference equation with oscillatory nonlinearityNonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz conditionThe application of the nonsmooth critical point theory to the stationary electrorheological fluidsExistence of one weak solution for \(p(x)\)-biharmonic equations with Navier boundary conditionsExistence of three solutions for equations of \(p(x)\)-Laplace type operators with nonlinear Neumann boundary conditionsMultiplicity of solutions for an anisotropic variable exponent problemMultiple solutions for a system involving an anisotropic variable exponent operatorRegularity theory for non-autonomous partial differential equations without Uhlenbeck structureVariational approaches to \(P(X)\)-Laplacian-like problems with Neumann condition originated from a capillary phenomenaA diffusion equation with a variable reaction orderThe existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary conditionOn a class of fractional Laplacian problems with variable exponents and indefinite weightsExistence and blow-up rate of large solutions of \(p(x)\)-Laplacian equations with gradient termsNon-autonomous eigenvalue problems with variable \((p_1,p_2)\)-growthOn a new fractional Sobolev space and applications to nonlocal variational problems with variable exponentLocal existence conditions for an equations involving the \(p(x)\)-Laplacian with critical exponent in \(\mathbb R^N\)A nonlinear eigenvalue problem with \(p(x)\)-growth and generalized Robin boundary value conditionMultiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spacesThe stability of the anisotropic parabolic equation with the variable exponentThe well-posedness of an anisotropic parabolic equation based on the partial boundary value conditionA-priori bounds and existence for solutions of weighted elliptic equations with a convection termExistence of multi-peak solutions for a class of quasilinear problems in Orlicz-Sobolev spacesCombined effects for non-autonomous singular biharmonic problemsExistence and multiplicity of solutions for \(p(x)\)-curl systems without the Ambrosetti-Rabinowitz conditionComparison and sub-supersolution principles for the fractional \(p(x)\)-LaplacianMultiple solutions of Neumann problems: an Orlicz-Sobolev space setting



Cites Work


This page was built for publication: Nonlinear elliptic equations with variable exponent: old and new