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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 1
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Original Articles

On the structure of the critical set of non-differentiable functions with a weak compactness condition

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Pages 1-10 | Received 17 Mar 2009, Accepted 09 Sep 2009, Published online: 19 Jan 2010

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K. Kefi, C. Nefzi, A. Alshammari & M. M. Al-Shomrani. (2024) Multiplicity of solutions for a non-local problem with indefinite weights. Applicable Analysis 103:8, pages 1387-1396.
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Jian Liu & Zengqin Zhao. p(x)-biharmonic equations involving Leray–Lions type operators with Hardy potentials. Complex Variables and Elliptic Equations 0:0, pages 1-14.
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Yu Tian & Weigao Ge. (2011) Multiple solutions of Sturm–Liouville boundary value problem via lower and upper solutions and variational methods. Nonlinear Analysis: Theory, Methods & Applications 74:17, pages 6733-6746.
Crossref
Salvatore Marano & Nikolaos Papageorgiou. (2011) On a Neumann problem with p -Laplacian and noncoercive resonant nonlinearity . Pacific Journal of Mathematics 253:1, pages 103-123.
Crossref
Yu Tian & Weigao Ge. (2011) Sign-changing and multiple solutions of the Sturm–Liouville boundary value problem via invariant sets of descending flow. Nonlinear Analysis: Theory, Methods & Applications 74:16, pages 5480-5494.
Crossref
GIUSEPPINA D'AGUÌ & GIOVANNI MOLICA BISCI. (2011) THREE NON-ZERO SOLUTIONS FOR ELLIPTIC NEUMANN PROBLEMS. Analysis and Applications 09:04, pages 383-394.
Crossref
Gabriele Bonanno, Giovanni Molica Bisci & Vicenţiu Rădulescu. (2011) Multiple solutions of generalized Yamabe equations on Riemannian manifolds and applications to Emden–Fowler problems. Nonlinear Analysis: Real World Applications 12:5, pages 2656-2665.
Crossref
Gabriele Bonanno, Giovanni Molica Bisci & Vicenţiu Rădulescu. (2011) Existence of three solutions for a non-homogeneous Neumann problem through Orlicz–Sobolev spaces. Nonlinear Analysis: Theory, Methods & Applications 74:14, pages 4785-4795.
Crossref
Gabriele Bonanno & Giovanni Molica Bisci. (2011) Three weak solutions for elliptic Dirichlet problems. Journal of Mathematical Analysis and Applications 382:1, pages 1-8.
Crossref
Pasquale Candito & Giuseppina D'Aguì. (2011) Three solutions to a perturbed nonlinear discrete Dirichlet problem. Journal of Mathematical Analysis and Applications 375:2, pages 594-601.
Crossref
JUNTAO SUN, HAIBO CHEN & TIEJUN ZHOU. (2010) MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATION VIA VARIATIONAL METHODS. Bulletin of the Australian Mathematical Society 82:3, pages 446-458.
Crossref
Gabriele Bonanno & Beatrice Di Bella. (2010) A fourth-order boundary value problem for a Sturm–Liouville type equation. Applied Mathematics and Computation 217:8, pages 3635-3640.
Crossref
Haibo Chen & Juntao Sun. (2010) An application of variational method to second-order impulsive differential equation on the half-line. Applied Mathematics and Computation 217:5, pages 1863-1869.
Crossref
Gabriele Bonanno & Stefania Maria Buccellato. (2010) TWO POINT BOUNDARY VALUE PROBLEMS FOR THE STURM-LIOUVILLE EQUATION WITH HIGHLY DISCONTINUOUS NONLINEARITIES. Taiwanese Journal of Mathematics 14:5.
Crossref
Gabriele Bonanno & Antonia Chinnì. (2010) Existence of three solutions for a perturbed two-point boundary value problem. Applied Mathematics Letters 23:7, pages 807-811.
Crossref
Gabriele Bonanno & Roberto Livrea. (2010) Multiple periodic solutions for Hamiltonian systems with not coercive potential. Journal of Mathematical Analysis and Applications 363:2, pages 627-638.
Crossref
Pasquale Candito & Giuseppina D'Aguì. (2010) Three Solutions for a Discrete Nonlinear Neumann Problem Involving the -Laplacian. Advances in Difference Equations 2010:1, pages 862016.
Crossref
Pasquale Candito & Giuseppina D'Aguì. (2010) Three Solutions for a Discrete Nonlinear Neumann Problem Involving the p-Laplacian. Advances in Difference Equations 2010, pages 1-11.
Crossref
Gabriele Bonanno & Giuseppina D'Aguì. (2010) Multiplicity Results for a Perturbed Elliptic Neumann Problem. Abstract and Applied Analysis 2010, pages 1-10.
Crossref
Wei Zhang & Jinbo Ni. (2022) Study on a New P-Laplacian Fractional Differential Model Generated by Instantaneous and Non-Instantaneous Impulsive Effects. SSRN Electronic Journal.
Crossref

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